Exercise 27 Page 682

In order to decide whether our friend is correct, we need to calculate the probability of the softball game to be rescheduled.

Finding the Probability

Let's consider two events.

• $A\text{:}$ it rains
• $B\text{:}$ the game will be rescheduled

We know that the game can be rescheduled only if it rains. Therefore, we need to look for the probability $P(\text{rains and rescheduled}),$ which can be denoted in the following way. Since the event of rescheduling the game is dependent on whether it rains, we will recall how to find the probability of dependent events.

Probability of Dependent Events

If two events A and B are dependent events, then the probability that both events occur is the product of the probability of the first event and the conditional probability of the second event given the first event. $P(A\text{ and }B)=P(A)\cdot P(B|A)$

We know that there is $70\%$ chance of rain, which corresponds to the probability of event $A.$ We are told that when it rains, there is $75\%$ chance that the softball game will be rescheduled. The probability that an event will occur given that another event has already occurred is called a conditional probability. Therefore, we can write the probability $P(B|A).$ With this information, we can calculate the $P(A\text{ and }B).$ We found that the probability of the softball game to be rescheduled is $52.5\%.$

Is the Friend Correct?

Our friend believes the game is more likely to be rescheduled than played. Let's recall the chance of the softball game to be rescheduled. Since the chance is greater than $50\%$ chance, we conclude that our friend is correct. The softball game is more likely to be rescheduled than played