**Overview**

Consider a situation-

“ Suppose there are 100 hospitals buying a vaccine for COVID-19, 40 of them ordered covaxin, 30 of them ordered covishield and 20 ordered covaxin and covishield. If one hospital is chosen at random ordered covaxin, then what is the probability it also ordered covishield”

So that here in this situation we need to find the probability of an event when another event has already happened, such types of probabilities are known as conditional probability.

**Definition**

The probability of an event X, such that event Y has already happened, is called conditional probability of X on the condition that Y has already happened .

We denote the conditional probability by P(X/Y) and we read it as the probability of X given Y.

Suppose there are two events X and Y of a sample space S and let P(Y) is non-zero then the conditional probability of event X, given Y is defined as-

Note-

When the events X and Y are independent, then-

Or

**Example: The probability of A hits the target is 1 / 4 and the probability that B hits the target is 2/ 5. If both shoot the target then find the probability that at least one of them hits the target.**

Here it is given that-

Now we have to find-

Both two events are independent. So that-

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