# 11.4.1. Calculating Probability

Given that and are two events of a random experiment, where , , and , determine .

• A0.3
• B0.18
• C0.94
• D0.24

### Example

Given that and are two events of a random experiment, where , , and , determine .

### Solution

The notation refers to the probability of the occurrence of and the non-occurrence of . Also, the notation refers to the probability of events and occurring together. For this reason, is equal to the sum of and First, solve for in terms of as follows:

The notation refers to the probability of the occurrence of and the non-occurrence of Another way to write it is For this reason, is equal to the sum of and Now use substitution to again solve for in terms of

Next, use substitution to solve for

Now solve for as follows:

Next, solve for

The notation refers to the probability of either event or event occurring, or both. If and are two non-mutually exclusive events, then where the notation refers to the probability of events and occurring together. Now use this fact to find

Thus, is equal to 0.3.

0
correct
0
incorrect
0
skipped