Exercise 64 Page 344

We want to know the intersection of students involved in a club and that study more than 4 hours a day. To make things a little easier, we will introduce a couple of variables. C&=in a club S&=study 4 or more hours a day From the exercise we know that students either involved in a club or study 4 hours a day or more make up 53.4 % of the sample. This describes the union, P(C or S), of these events. To calculate this probability, we have to add the probabilities of P(C) and P(S) and subtract their intersection. P(C or S)=P(C)+P(S)-P(C and S) From the exercise we have been given the following information. P(C)=35.7 % [0.7em] P(S)=27.8 % [0.7em] P(C or S)=53.4 % Now we can find the probability of the union of college students involved in a club and who study 4 or more hours per day.

P(C or S)=P(C)+P(S)-P(C and S)

SubstituteValues

Substitute values

53.4 %=35.7 % +27.8 %-P(C and S)

AddTerms

Add terms

53.4 %=63.5 %-P(C and S)

SubEqn

LHS-63.5 %=RHS-63.5 %

- 10.1 %=- P(C and S)

MultEqn

LHS * (- 1)=RHS* (- 1)

10.1 %=P(C and S)

RearrangeEqn

Rearrange equation

P(C and S)=10.1 %