Exercise 34 Page 930

Recall that the sum of probabilities of events is equal to 1 only when together they are the whole sample space.

There can be more events in the sample space.

Practice makes perfect

When two events are mutually exclusive they cannot happen at the same time. Let's consider an example of rolling a die.

Here, rolling 1 and rolling 6 are mutually exclusive events because we cannot roll 1 and 6 at the same time using one die. However, since the probability of rolling each number is 16, the sum of the probabilities of these two events is not equal to 1. 1/6+ 1/6≠ 1 This is because we have other possible outcomes in the sample space. If we would add the probabilities of all 6 possible outcomes, then it would give us 1.

P_1+P_2+P_3+P_4+P_5+P_6

SubstituteValues

Substitute values

1/6+ 1/6+ 1/6+ 1/6+ 1/6+ 1/6

▼

Simplify

AddFrac

Add fractions

1+1+1+1+1+1/6

AddTerms

Add terms

6/6