Chapter 10.4, Problem 19E

To determine

Tocalculate:

The probability that you miss the announcement or question.

Answer to Problem 19E

The probability that you miss the announcement or question is $0.22$ .

Explanation of Solution

Given information:

Random time to announces the song between $=7:00$ and $7:30A.M.$

Random time to ask trivia quetion between $=7:15$ and $7:45A.M.$

Time when anyone listen $=7:20$

Calculation:

Assume that event $A$ denote announcement of the song of the day and event $B$ denote asking the trivia question. This implies there is $30$ minutes for the song of the day, $30$ minutes for the trivia question, $15$ minutes during which both might occur.

Since, one starts listening the radio station at $7:20A.M.$ , it implies that either of the two events occur during $25$ minutes.

Therefore,the probability that one listens the song of the day and also the trivia questions is as follows:

  $\begin{array}{l}P\left(AandB\right)=P\left(A\right)+P\left(B\right)-P\left(AorB\right)\\ =\frac{30}{45}+\frac{30}{45}-\frac{25}{45}\\ =0.78\end{array}$

Thus, the probability that one misses the song of the day and also the trivia question is as follows:

  $\begin{array}{l}P\left(AandB\right)\text{'}=1-P\left(AandB\right)\\ =1-0.78\\ =0.22\end{array}$

Hence, the answer is $0.22$ .

So, the probability that you miss the announcement or question is $0.22$ .