Chapter 10.2, Problem 27E

To determine

To explain:

The prediction given by your friend is correct or not for the softball game

Answer to Problem 27E

Yes, friend’s prediction for the rescheduling game is correct as the chances of rescheduling of softball game are $52.5\%$ greater than $50\%$ .

Explanation of Solution

Given information:

Probability of raining: $70\%=0.7$

Probability to reschedule the softball game: $75\%=0.75$

Consider,

Probability of raining: $P\left(A\right)=0.7$

Probability to reschedule the softball game: $P\left(B\right)=0.75$

Now, the probability value reschedule the softball game due to raining as per claim by meteorologist is calculated as:

  $\begin{array}{l}P\left(A\cap B\right)=P\left(A\right)\times P\left(B\right)\\ P\left(A\cap B\right)=0.7\times 0.75\\ P\left(A\cap B\right)=0.525\\ P\left(A\cap B\right)=52.5\%\end{array}$

So, the chances of rescheduling of softball game are $52.5\%$ , making it greater than $50\%$ . That’s why, prediction by your for the rescheduling game is correct.