Introduction to Basic Probability #1

In this post we will get an introduction to basic Probability and what it entails. Statistics and Probability are two topics that go hand in hand. We always need to study and understand probability before venturing into statistics.

What is Probability?

Probability is defined as the likelihood of occurrence of a specified (desired or undesired) event. The most common usage of probability that can be told globally is the chance of rainfall on any given day. You will notice in your weather app that the chance of rainfall is given as a percentage value, anywhere between 0% to 100%. If you ask someone a question, such as ” are you attending the class tomorrow?” and they answer “probably”, then there is a chance that the person may not attend the class. If we try to calculate this mathematically, then we are solving his probability of attending the class.

Probability of any event will always have its value between 0(Zero) and 1, Or 0% and 100% if you convert the probability into percentages. 0 and 1 are the extreme cases of probability. If an event has 0 probability. then it will not occur. and if it has 1.0 as probability, it is certain to occur.

It becomes easy to explain probability with the use of working examples.

Examples on basic probability

The Classic Coin Toss

You will notice that most available books and online courses go with the coin toss, because it is the easiest of the probability examples. Where you can have only 2 outcomes. Heads and Tails. each outcome has an equal likelihood of occurring. So P(heads) = 0.50 and P(tails) = 0.50. This may also be expressed as a percentage. P(heads) = 50% and P(tails) = 50%

Simple Dice.

A normal board game dice has 6 sides, showing the numbers 1 to 6 on the faces. A balanced die will show each number with equal likelihood. Since there are 6 outcomes of the dice throw, the probability of each event is

P dice - Introduction to basic probability

School Students

Here is another classic problem given for probability basics. There is a school with a certain number of students and they have a certain characteristic of interest to the observer. lets look at the given data.

P school - introduction to Basic Probability

The data shows that the event of interest is Chicken Pox. If you were to pick a student at random, what is the probability that they had chicken pox? In this problem. the answer will be P(yes) = 155/210 = 0.738 (or 73.8%). We see that there is 73% chance that the random student we pick will have had chicken pox.

What is the probability that a randomly picked student is a boy? P(boy) = 100/210 = 0.476 (or 47.6%).

What is the probability that you pick a girl who did not have chicken pox? P (G no CP) = 30/210 = 0.143 (or 14.3%)

Notice that the number of girls that did not get chicken pox is very small as compared to the total number of students. So the likelihood of randomly picking out one that fits is also low.

This tells us that Probability values that are closer to 0.0 are less likely to occur. Probability values closer to 1.0 are more likely to occur.

Categories of Basic Probability

We can divide basic probability in two categories. 1) unconditional probability and 2) conditional Probability.

Unconditional Probability

When we compare our event of interest in the probability experiment, with the whole population, it is known as unconditional probability. We worked with unconditional probability in the above school example. The denominator in every equation is the total population (210).

Conditional Probability

In many experiments we need specialized probability values based on a condition occurring first. It is know as Conditional Probability and is denoted as P(A|B). this means we are looking for probability of A given B has occurred.

What is the Probability of picking a boy given he did not have chickenpox. P(Boy|No CP) = 25/55 = 0.454 (or 45.4%). Note that the event that has occurred is now in the denominator in this case.

What is the probability that you picking someone who had chicken pox given its a girl?
P(CP|girl) = 80/110 = 0.727 (or 72.7%)

You can find more problems on basic Probability here.

Click here for Part 2.

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