Question

during final exam weeks, many college students exercise to fuel their study sessions. data from a recent survey are shown in the venn diagram. let m be the event that the student exercises in the morning and let a be the event that the student exercises in the afternoon. what is the probability that a randomly chosen college student does not exercise in the morning? 0.14 0.24 0.38 0.75

Explanation:

Step1: Calculate the probability of exercising in the morning

The probability of exercising in the morning \(P(M)\) is the sum of the part only in \(M\) and the intersection of \(M\) and \(A\). So \(P(M)=0.25 + 0.37=0.62\).

Step2: Use the complement rule

The probability of an event \(E\) not occurring is \(P(\overline{E})=1 - P(E)\). Here, if \(E\) is the event of exercising in the morning, then the probability of not exercising in the morning \(P(\overline{M})\) is \(1-0.62 = 0.38\).

Answer:

0.38