# What is the probability of A and B?

**B**are independent, then the

**probability**that events A and

**B**both occur is: p(A and

**B**) = p(A) x p(

**B**). In other words, the

**probability of A and B**both occurring is the product of the

**probability**of A and the

**probability**of

**B**. Therefore, the

**probability**of both events is: 1/52 x 1/4 = 1/208 .

Hereof, how do you find the probability of A and B?

**Formula** for the **probability of A and B** (independent events): p(A and **B**) = p(A) * p(**B**). If the **probability** of one event doesn't affect the other, you have an independent event. All you do is multiply the **probability** of one by the **probability** of another.

**B**are two events in a sample space S, then the conditional

**probability of A given B**is defined as P(A|

**B**)=P(A∩

**B**)P(

**B**), when P(

**B**)>0.

Subsequently, one may also ask, what is the probability of A or B or both?

The **probability** that Events A and **B both** occur is the **probability** of the intersection of A and **B**. The **probability** of the intersection of Events A and **B** is denoted by P(A ∩ **B**). If Events A and **B** are mutually exclusive, P(A ∩ **B**) = 0.

To test **whether** two events A and **B are independent**, calculate P(A), P(**B**), and P(A ∩ **B**), and then **check whether** P(A ∩ **B**) equals P(A)P(**B**). **If** they are equal, A and **B are independent**; **if** not, they are dependent.