Conditional probability distribution

Imagine you have a big jar filled with different colored candies. Let's say you have red, green, and blue candies. Now, let's imagine that you want to figure out the probability of picking a red candy from the jar.

First, you need to count the total number of candies in the jar. Let's say there are 30 candies in total.

Out of those 30 candies, let's say there are 10 red candies. This means that the probability of picking a red candy is 10/30 or 1/3.

Now, let's say that you want to figure out the probability of picking a red candy, given that you already know the candy is either red or green. This is where conditional probability comes in.

To calculate the conditional probability, you need to use the formula:

Conditional probability = Probability of both events happening / Probability of one event happening

In this case, the events are picking a red candy and the candy being either red or green.

So, let's say you randomly picked a candy from the jar, and it turned out to be either red or green. This means there are only 20 possible candies left in the jar. Out of these, 10 are red and 8 are green.

Now, you want to figure out the probability of picking a red candy, given that the candy is either red or green.

The probability of both events happening is the number of red candies in the jar, which is 10.

The probability of one event happening (either picking a red or green candy) is the number of red and green candies in the jar, which is 18.

So, the conditional probability of picking a red candy, given that the candy is either red or green is:

Conditional probability = 10/18 or 5/9

This means that if you know the candy is either red or green, the probability of it being red is actually higher than if you didn't know anything about the candy's color beforehand.

This is the basic idea of conditional probability, where you calculate the probability of an event given that you know something about another event.