To confirm if the two events are independent when solving a problem is useful. This ensures that you are using the correct solving method. Example 4 explains how to do this.

Every year, 42% of students catch the flu. Every year 21% of students get the flu shot. 10% of those that get the shot catch the flu. Are getting a flu shot and getting the flu independent?

You know that, for independent events, P ( A and B ) = P ( A ) x P ( B ). Test the values given in the question to see if they fit this equation.

P (getting flu shot and catching the flu) = 10% = 0.1

P (getting flu shot) x P (catching the flu) = 21% ?- 42% = 0.21 ?- 0.42 = 0.0882

Because the answers are not equal, they do not fit equation P ( A and B ) = P ( A ) x P ( B ). The events are not independent.

 

Complete the questions on page 198 (5a & 5b) for more practice in testing whether two events are independent.

Click here to verify your answers .