Name: What is probability | Expected Values, Frequency Distribution, Complement
Uploaded: 2020-03-28T09:10:45.000Z
Duration: 20 min 46 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Basic passive voice

Life is filled with uncertain events and often we must consider the possible outcomes before

We ask ourselves questions like “What is the chance of success?” and “What is the

probability that we fail?” to determine whether the risk is worth taking.

Many CEOs need to make huge decisions when investing in their research and development

departments or contemplating buyouts or mergers.

By using probability and statistical data, they can predict how likely each outcome is

Some of you might be wondering: “What is this probability we are talking about?”.

Essentially, probability is the chance of something happening.

A more academic definition for this would be “the likelihood of an event occurring”.

The word event has a specific meaning when talking about probabilities.

Simply put, an event is a specific outcome or a combination of several outcomes.

These outcomes can be pretty much anything - getting Heads when flipping a coin, rolling

a 4 on a six-sided die or running a mile in under 6 minutes.

There isn’t only one single probability involved since there are two possible outcomes:

That means we have two possible events and need to assign probabilities to each one.

When dealing with uncertain events we are seldom satisfied by simply knowing whether

Ideally, we want to be able to measure and compare probabilities in order to know which

To do so, we express probabilities numerically.

Even though we can express probabilities as percentages or fractions, conventionally we

write them out using real numbers between 0 and 1.

So, instead of using 20% or one fifth, we prefer 0.2.

Now let us briefly talk about interpreting these probability values.

Having a probability of ‘1’ expresses absolute certainty of the event occurring

and a probability of ‘0’ expresses absolute certainty of the event NOT occurring.

You probably figured this out, but higher probability values indicate a higher likelihood.

As you can imagine, most events we are interested in would have a probability other than 0 and

So, values like 0.2, 0.5, and 0.66 are what we generally expect to see.

Even without knowing any of this, you can tell some events are more likely than others.

For instance, your chance of winning the lottery isn’t as great as winning a coin toss.

That’s why you can think of probability as a field that is about quantifying exactly

how likely each of those events are on their own.

Generally, the probability of an event A occurring, denoted P of A, is equal to the number of

preferred outcomes over the total number of possible outcomes.

By preferred we mean outcomes that we want to see happen.

A different term people use for such outcomes is “favourable”.

Similarly, sample space, is a term used to depict all possible outcomes.

Going forward, we shall use the respective terms interchangeably.

We will go through several examples to ensure you understand the notion well.

Say, event A is flipping a coin and getting Heads.

In this case, Heads is our only preferred outcome.

Assuming the coin doesn’t just somehow stay in the air indefinitely, there are only 2

This means that our probability would be a half, so we write the following:

P of getting Heads, equals one half, which equals 0.5.

Now, imagine we have a standard six-sided die and we want to roll a 4.

Once again, we have a single preferred outcome, but this time we have a greater number of

Therefore, the probability of this event would look as follows:

P of rolling 4 equals: one sixth, or approximately 0 point one six seven.

Events can be simple, or a bit more complex.

For example, what if we wanted to roll a number divisible by 3?

That means we need to get either a 3 or a 6 so the number of preferred outcomes becomes

However, the total number of possible outcomes stays the same since the die still has 6 sides.

Therefore, we conclude that the probability of rolling a number divisible by 3 equals:

Note that the probability of two independent events occurring at the same time, is equal

to the product of all probabilities of the individual events.

For instance, the likelihood of getting the Ace of Spades equals the probability of getting

an Ace, times the probability of getting a spade.

Expected values represent what we expect the outcome to be if we run an experiment many

To fully grasp the concept, we must first explain what an experiment is.

Imagine we don’t know the probability of getting heads when flipping a coin.

We are going to try to estimate it ourselves, so we toss a coin several times.

After doing one flip and recording the outcome we complete a trial.

By completing multiple trials, we are conducting an experiment.

For example, if we toss a coin 20 times and record the 20 outcomes, that entire process

The probabilities we get after conducting experiments are called experimental probabilities,

whereas the ones we introduced earlier were theoretical or true probabilities.

Generally, when we are uncertain what the true probabilities are or how to compute them,

The experimental probabilities we get are not always equal to the theoretical ones but

For instance, eight out of ten times I go to my local shop, I have to wait in line.

Based on my experience, 80% of the time there will be a queue and 20% of the time, there

I can try to calculate the true probability, but it would include far too many factors.

The experimental probability, on the other hand, is easy to compute and very useful.

The formula we use to calculate experimental probabilities is similar to the formula applied

for the theoretical ones earlier in the course.

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What is probability | Expected Values, Frequency Distribution, Complement

specific

individual

guarantee

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