Complementary event

Hello! Let me explain to you what a complementary event means.

Imagine you have two boxes, one with red balls and one with blue balls. You want to pick one ball from one of the boxes, but you can only choose one. What are the chances of getting a red ball? What are the chances of getting a blue ball?

Now, let's say that all the balls in the two boxes are either red or blue. This means that the chances of picking a red ball and a blue ball are the only two options you have. And here's where the complementary event comes in!

The complementary event is the opposite of the event that you are interested in. In this case, the event we are interested in is picking a red ball. The complementary event would be picking a blue ball.

So, if you want to find out the probability of picking a red ball, you can simply subtract the probability of picking a blue ball from 1 (since there are only two options - red or blue). This is because the sum of the probabilities of all possible outcomes must equal 1.

In other words, if the probability of picking a red ball is 0.7, then the probability of picking a blue ball (the complementary event) would be 0.3 (1 - 0.7 = 0.3).

So, the complementary event is simply the opposite of the event you are interested in, and you can use it to find out the probability of the desired event by subtracting it from 1. I hope this explanation made sense to you!