THE LAW OF PROBABILITY - Probability equals the number of ways a specified event can occur, divided by the total number of all possible event occurrences. Probability can only range from values 0 to 1. A probability of 0 means there are no possible outcomes for that event - a probability of 1 means the event will occur in each and every trial - Probability measures the likelihood of an event occurring. If you have a bag containing three marbles -- one blue marble and two green marbles -- the probability of grabbing a blue marble sight unseen is 1/3. There is one possible outcome where the blue marble is selected, but three total possible trial outcomes -- blue, green, and green. Using the same math the probability of grabbing a green marble is 2/3. You can discover the unknown probability of an event through experimentation. Using the previous example, say you do not know the probability of drawing a certain colored marble, but you know there are three marbles in the bag. You perform a trial and draw a green marble. You perform another trial and draw another green marble. At this point you might claim the bag contains only green marbles, but based on two trials, your prediction is not reliable. It is possible the bag contains only green marbles or it could be the other two are red and you selected the only green marble sequentially. If you perform the same trial 100 times you will probably discover you select a green marble around 66% percent of the time.

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The Law of Probability

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Probability equals the number of ways a specified event can occur, divided by the total number of all possible event occurrences. Probability can only range from values 0 to 1. A probability of 0 means there are no possible outcomes for that event - a probability of 1 means the event will occur in each and every trial

By Andrea Farkas

Probability measures the likelihood of an event occurring.

Expressed mathematically, probability equals the number of ways a specified event can occur, divided by the total number of all possible event occurrences.

For example, if you have a bag containing three marbles -- one blue marble and two green marbles -- the probability of grabbing a blue marble sight unseen is 1/3.

There is one possible outcome where the blue marble is selected, but three total possible trial outcomes -- blue, green, and green.

Using the same math the probability of grabbing a green marble is 2/3.

Law of Large Numbers

You can discover the unknown probability of an event through experimentation.

Using the previous example, say you do not know the probability of drawing a certain colored marble, but you know there are three marbles in the bag.

You perform a trial and draw a green marble. You perform another trial and draw another green marble.

At this point you might claim the bag contains only green marbles, but based on two trials, your prediction is not reliable.

It is possible the bag contains only green marbles or it could be the other two are red and you selected the only green marble sequentially.

If you perform the same trial 100 times you will probably discover you select a green marble around 66% percent of the time.

This frequency mirrors the correct probability more accurately than your first experiment.

This is the law of large numbers: the greater the number of trials, the more accurately the frequency of an event's outcome will mirror its actual probability.

Law of Subtraction

Probability can only range from values 0 to 1.

A probability of 0 means there are no possible outcomes for that event.

In our previous example, the probability of drawing a red marble is zero.

A probability of 1 means the event will occur in each and every trial.

The probability of drawing either a green marble or a blue marble is 1.

There are no other possible outcomes.

In the bag containing one blue marble and two green ones, the probability of drawing a green marble is 2/3.

This is an acceptable number because 2/3 is greater than 0, but less than 1-- within the range of acceptable probability values.

Knowing this, you can apply the law of subtraction, which states if you know the probability of an event, you can accurately state the probability of that event not occurring.

Knowing the probability of drawing a green marble is 2/3, you can subtract that value from 1 and correctly determine the probability of not drawing a green marble: 1/3.

Law of Multiplication

If you want to find the probability of two events occurring in sequential trials, use the law of multiplication.

For example, instead of the previous three-marbled bag, say there is a five-marbled bag.

There is one blue marble, two green marbles, and two yellow marbles.

If you want to find the probability of drawing a blue marble and a green marble, in either order (and without returning the first marble to the bag), find the probability of drawing a blue marble and the probability of drawing a green marble.

The probability of drawing a blue marble from the bag of five marbles is 1/5.

The probability of drawing a green marble from the remaining set is 2/4, or 1/2.

Correctly applying the law of multiplication involves multiplying the two probabilities, 1/5 and 1/2, for a probability of 1/10.

This expresses the likelihood of the two events occurring together.

Law of Addition

Applying what you know about the law of multiplication, you can determine the probability of only one of two events occurring.

The law of addition states the probability of one out of two events occurring is equal to the sum of the probabilities of each event occurring individually, minus the probability of both events occurring.

In the five-marbled bag, say you want to know the probability of drawing either a blue marble or a green marble.

Add the probability of drawing a blue marble (1/5) to the probability of drawing a green marble (2/5). The sum is 3/5.

In the previous example expressing the law of multiplication, we found the probability of drawing both a blue and green marble is 1/10.

Subtract this from the sum of 3/5 (or 6/10 for easier subtraction) for a final probability of 1/2.

Andrea Farkas has been writing since 2005. Her legal article appears in the "Texas Tech Estate Planning" and "Community Property Law Journal." Farkas graduated from Texas A&M University and earned her law degree from Texas Tech University School of Law.

https://sciencing.com/law-probability-8657085.html

TRAVEL FATIGUE - The feeling of tiredness in cars, buses or even airplanes is quite subjective, and as such, may not apply in every case. There may be people who DO NOT find traveling in a bus over long distances tiring. When you’re traveling on a road, your car/bus is bound to accelerate/decelerate countless times, thanks to the natural flow of traffic. The vehicle will also take many turns, which are bound to repeatedly sway you from one side to another. In addition to the turns, swaying and constant changes in speed, there are a few other factors at play, such as the condition of the automobile, passenger seats and even the quality of the roads. All of these factors have a cumulative effect on passenger comfort. You don’t realize it actively, but the constant sways and changes in speed cause you to remain upright. Your brain keeps your muscles engaged to account for these movements of the vehicle to ensure that your posture is properly maintained. These small movements cause your muscles to constantly work, which makes them tired over a long journey — one that lasts for more than 2-3 hours. Just because you don’t realize it actively, that doesn’t mean your muscles are just ‘sitting’ there, doing nothing. In fact, this is the reason why standing still hurts your legs more than walking. Trains, on the other hand, are comparatively less tiring. The reason is simple: they don’t accelerate/decelerate and change directions as frequently as automobiles on the road.

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Travel Fatigue

Why Does Traveling Tire You Out?

By Ashish

Your brain keeps your muscles engaged to account for small movements of the vehicle to ensure that your posture is properly maintained.

These small movements cause your muscles to constantly work, which makes them tired over a long journey.

I have a few friends who like to go on long road trips. They want to just hop in their cars and drive a few hundred miles without a care in the world!

Me? I’m not like that at all.

Those people who do find me shying away from road trips simply because I find them too tiring often ask me what my deal is with traveling long distances in cars or by bus.

I admit that I have, more than once, given a lot of thought to this — why do people get tired when they travel long distances in certain vehicles?

They’re basically just sitting there, doing nothing, right? Why should that be any different than sitting in a train or even sitting in a chair in your house?

Note: The feeling of tiredness in cars, buses or even airplanes is quite subjective, and as such, may not apply in every case.

There may be people who DO NOT find traveling in a bus over long distances tiring.

This article only presents a few factors that largely contribute to making one feel tired after a long journey in a car, bus or commercial jet.

Factors that impact passenger comfort on the road

When you’re traveling on a road, your car/bus is bound to accelerate/decelerate countless times, thanks to the natural flow of traffic.

A bus changes its speed many times, causing its passengers
to feel this movement/pulse in very subtle ways.

In addition to that, the vehicle will also take many turns, which are bound to repeatedly sway you from one side to another.

In addition to the umpteen turns, swaying and constant changes in speed, there are a few other factors at play, such as the condition of the automobile, passenger seats and even the quality of the roads.

All of these factors have a cumulative effect on passenger comfort.

You don’t realize it actively, but the constant sways and changes in speed cause you to remain upright.

Your brain keeps your muscles engaged to account for these movements of the vehicle to ensure that your posture is properly maintained.

This guy probably wouldn’t look so upbeat if he were to sit
in the same seat for 10 hours or more, thanks to the tiredness
 that almost feels inherent on such long road journeys.

These small movements cause your muscles to constantly work, which makes them tired over a long journey — one that lasts for more than 2-3 hours.

Just because you don’t realize it actively, that doesn’t mean your muscles are just ‘sitting’ there, doing nothing.

In fact, this is the reason why standing still hurts your legs more than walking.

Here’s an interesting fact: Greger Huttu — a world champion of iRacing (a virtual racing simulator) — was invited to drive a real race car.

He went a few laps very fast (nearly 100mph), but then threw up in his helmet because his body couldn’t handle the tremendous physical forces acting on it. He gave up in his 15th lap.

Believe it or not, but car racing can be very tiring… physically.

Contrary to what one might think, driving race cars takes a toll on drivers’ bodies. That’s why F1 racers work out so much to stay in shape and handle those enormous G forces.

Trains, on the other hand, are comparatively less tiring.

The reason is simple: they don’t accelerate/decelerate and change directions as frequently as automobiles on the road. Thus, train journeys aren’t that tiring.

Fatigue-causing factors in a flight

Flights are no better when it comes to causing fatigue.

One might say that airplanes don’t experience rapid changes in speeds like cars do, so traveling in airplanes shouldn’t be so tiring, right?

Well, there are other factors that wear you out in a plane.

First, there’s the ‘height’ thing… your body has to adjust to being higher up really quick.

Although the cabin pressure makes it a little easier for your body to adjust to the altitude change, it still is far from what you’d call ‘normal’, i.e., something you experience sitting in a chair in your bedroom.

Then, there’s the case of dehydration.

In order to maintain pressure within the cabin, airlines must closely regulate the air inside. This involves changing the composition of the breathable air inside the cabin.

Cabin air is drier than ‘normal’ air.

This is why the cabin air is 15% drier than ‘ground air’, which makes passengers dehydrated. In fact, this is one of the many reasons that airplane food tastes so bad.

Furthermore, you can’t forget the way a plane moves.

All that noise, shuddering, rolling, turbulence and other vibrations you experience during a flight are not natural movements for the human body.

The body constantly tries to stabilize itself, which causes fatigue, which is why you feel tired after a long flight, even though on the surface it looks as though you were just sitting there in your seat doing nothing.

The psychological factor

One cannot disregard the psychological aspect of traveling over long distances. The very idea of traveling wears a lot of people out.

When traveling on a flight, you’re probably a bit conscious of yourself and your surroundings.

There are strangers all around you, and you subconsciously try to stay out of their personal space.

In other words, you’re constantly on ‘alert’ or worried, which is not (most) people’s natural state of mind. This adds to the mental exhaustion of traveling for hours in a flight.

That’s why business class in flights is such a popular thing. You get more space up there, and it’s way more comfortable.

The whole point of business class is to make you feel at home, so that you’re well rested and ready to work the moment you step off the aircraft.

The feeling of tiredness is very subjective, however, and differs from one person to another.

For those people who DO get tired during long road trips or flights, these are some of the key factors that contribute to their fatigue.

Ashish is a Science graduate (Bachelor of Science) from Punjabi University (India). He spends a lot of time watching movies, and an awful lot more time discussing them. He likes Harry Potter and the Avengers, and obsesses over how thoroughly Science dictates every aspect of life… in this universe, at least.

ScienceABC.com was launched with the sole objective of finding and sharing fun and interesting science facts. We believe that Science is a fascinating and valuable area of study for people of all ages, and we’re not alone! This website is curated by a team of professionals who are passionate about Science. Our greatest hope is that the fun we have curating this content is the same for everyone who reads it.

To quench the thirst of human curiosity about everything that happens around us in the environment and universe.

https://www.scienceabc.com/humans/travel-fatigue-why-does-traveling-tire-you-out.html

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PROBIOTICS AND SIDE EFFECTS - Probiotics are healthful strains of live bacteria and yeast. Taking probiotics can provide a range of benefits, but it can also cause side effects. Trillions of bacteria and other microorganisms live in the gut. Scientists refer to this community of gut-dwelling organisms as the gut microbiota. Research indicates that this microbiota plays an important role in digestion and gut health, while supporting the immune system, for example. Some bacteria benefit their human hosts, while other types cause harm. Disturbing the natural balance of bacteria in the gut can lead to digestive problems, infections, and other issues. Studies suggest that consuming probiotics can provide more healthful bacteria, which may help restore the balance of the gut microbiota. Some yogurts, supplements, and fermented foods, including kefir, sauerkraut, and tempeh, contain probiotics. The most common probiotics that manufacturers add to commercial products are species of Bifidobacterium and Lactobacillus bacteria. Research suggests that probiotics may help manage gastrointestinal conditions, including irritable bowel syndrome (IBS) and inflammatory bowel disease (IBD). Many people use probiotics to help treat episodes of diarrhea and constipation. Though taking probiotics may provide various benefits, it can also cause side effects.

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A person may experience gas and bloating when first using probiotics.

Probiotics And Side Effects

Can probiotics cause side effects?

Debra Rose Wilson

Probiotics are healthful strains of live bacteria and yeast. Taking probiotics can provide a range of benefits, but it can also cause side effects.

In this article, we discuss what probiotics are, how they promote health, and how to take them safely.

What are probiotics?

Trillions of bacteria and other microorganisms live in the gut. Scientists refer to this community of gut-dwelling organisms as the gut microbiota.

Research indicates that this microbiota plays an important role in digestion and gut health, while supporting the immune system, for example.

Some bacteria benefit their human hosts, while other types cause harm. Disturbing the natural balance of bacteria in the gut can lead to digestive problems, infections, and other issues.

Studies suggest that consuming probiotics can provide more healthful bacteria, which may help restore the balance of the gut microbiota.

Some yogurts, supplements, and fermented foods, including kefir, sauerkraut, and tempeh, contain probiotics.

The most common probiotics that manufacturers add to commercial products are species of Bifidobacterium and Lactobacillus bacteria.

A range of probiotic supplements and yogurts are available to purchase online.

Benefits of probiotics

Research suggests that probiotics may help manage gastrointestinal conditions, including irritable bowel syndrome (IBS) and inflammatory bowel disease (IBD).

Many people use probiotics to help treat episodes of diarrhea and constipation.

There is also evidence that probiotics may help with:

·               eczema

·               obesity

·               insulin resistance

·               type 2 diabetes

·               nonalcoholic fatty liver disease

·               improving immune system function

Possible side effects

Though taking probiotics may provide various benefits, it can also cause side effects, including:

Digestive symptoms

When first using probiotics, some people experience gas, bloating, or diarrhea. Changes in the gut microbiota can result in bacteria producing more gas than usual, which can lead to bloating.

However, these side effects usually clear up within a few days or weeks of taking the probiotics. If the symptoms persist, speak with a doctor, who can explore the possible causes.

In some cases, the doctor may recommend switching to a different probiotic.

Skin problems

In rare cases, probiotics may cause skin rashes or itchiness.

Authors of a 2018 review found that two study participants who took probiotics to treat IBS reported an itchy rash as a side effect. This led one participant to drop out of the trial.

If a rash or severe itching occurs, stop using the probiotic. Check the product’s labeling for any possible allergens, and see a doctor if the rash is severe, persistent, or it accompanies other concerning symptoms.

Once the rash has cleared, a person can try a different product or strain of probiotic.

Allergy risk

Anyone with an allergy or intolerance for gluten, soy, eggs, dairy, or lactose may need to exercise caution when choosing probiotics.

As with any supplement, always check ingredients lists to ensure that there is no risk of an allergic reaction. Some manufacturers offer allergen-free probiotics.

Anyone experiencing symptoms of an allergic reaction should stop using the probiotic immediately. Seek medical care if the reaction is severe.

Increased risk of infection

Although probiotics are generally safe to use, findings of a review from 2017 suggest that children and adults with severe illnesses or compromised immune systems should avoid using probiotics.

Some people with these conditions have experienced bacterial or fungal infections as a result of probiotic use.

If a person has a condition that affects their immune system, they should speak with their doctor before taking probiotics.

Also, anyone using antifungal medication should wait until the infection has cleared up before taking probiotics.

Small intestine bacterial overgrowth (SIBO)

The small and large intestines usually contain different types of bacteria. SIBO occurs when bacteria from the large intestine start growing in the small intestine.

The large intestine predominantly contains anaerobic bacteria, which do not require oxygen and live by fermenting indigestible carbohydrates from plant-based foods as they pass through the gut.

Symptoms of SIBO are similar to those of IBS, including gas, bloating, and diarrhea. SIBO can also cause brain fogginess and short-term memory problems.

Not everyone with IBS has SIBO, but the overgrowth is more common in people with IBS. SIBO also frequently develops in older females.

Experts do not fully understand what causes the overgrowth, but it may result from reduced gut motility, which slows the passage of food through the gut.

This can cause fermentable carbohydrates to remain in the small intestine for longer.

Results of a 2018 study indicate a possible link between SIBO and probiotic supplementation in people with brain fogginess.

The researchers found that symptoms improved when participants stopped taking probiotics and started taking antibiotics.

Anyone with SIBO symptoms should consult a doctor.

Antibiotic resistance

Rarely, probiotic bacteria can contain antibiotic-resistant genes. They can pass these genes on to other strains of bacteria, including the harmful strains that cause infections.

However, manufacturers systematically test commercial probiotics stains for the presence of antibiotic resistance.

To reduce the risk of consuming antibiotic-resistant bacteria, always source probiotics from trusted, reputable manufacturers.

Bottom of Form

How to take probiotics safely

Little evidence suggests that a person can overdose on probiotics. However, always read labeling carefully and do not exceed the manufacturer’s recommended dosage.

The optimal dosage can vary, depending on a person’s health and the type of probiotic product.

If a probiotic causes any side effects or symptoms, consider reducing the dosage or refraining from taking the product.

Summary

Probiotics are beneficial strains of live bacteria or yeast. Regularly taking probiotics can help restore the natural balance of the gut microbiota.

It may also help treat a number of health conditions, including IBS and IBD.

Probiotics are generally safe, and any side effects are usually mild and short-lived.

However, if a symptom is causing concern, consider reducing the probiotic’s dosage, trying a different strain, or stopping use altogether.

Consult a doctor about any severe or persistent side effects.

Before using any probiotic product, read the instructions carefully and do not exceed the maximum dosage. People with allergies should also check labeling for potential triggers.

Probiotics are found in many common foods, and a variety of types of healthy bacteria are available from the diet alone.

If you are considering taking probiotic supplements, research your manufacturer.

The FDA do not monitor supplements, so it is wisest to buy from a reputable drugstore or health food chain. Always check expiry dates.

Check the colony forming units (CFU) on the bottle to see the amount of bacteria in the dose, and follow the manufacturer’s guidelines for how much to take. Some probiotic supplements require storage in a refrigerator.

Debra Rose Wilson, PhD, MSN, RN, IBCLC, AHN-BC, CHT

https://www.medicalnewstoday.com/articles/323821#side-effects