Chapter 5.2, Problem 48E

To determine

Probability that the person reads the Los Angeles Times or the Wall Street Journal .

Answer to Problem 48E

Probability that the person reads one of the two newspapers is 60%

Explanation of Solution

Given:

40% of the guests read the Los Angeles Times .

25% of the guests read the Wall Street Journal .

5% of the guests read both the newspapers.

For any two events,

General addition rule:

  $\text{P}\left(\text{A}\cup \text{B}\right)=\text{P}\left(\text{A}\right)+\text{P}\left(\text{B}\right)-\text{P}\left(\text{A}\cap \text{B}\right)$

Now,

Probability that the person reads Los Angeles Times ,

  $\text{P}\left(LAT\right)=40\%=0.40$

Probability that the person reads Wall Street Journal ,

  $\text{P}\left(WSJ\right)=25\%=0.25$

Probability that the person reads both the newspapers,

  $\text{P}\left(LAT\cap WSJ\right)=5\%=0.05$

Then

  $\text{P}\left(LAT\cup WSJ\right)=\text{P}\left(LAT\right)+\text{P}\left(WSJ\right)-\text{P}\left(LAT\cap WSJ\right)$

  $\begin{array}{l}\text{P}\left(LAT\cup WSJ\right)=0.40+0.25-0.05\\ =0.60\\ =60\%\end{array}$

Therefore,

Probability that the person reads the Los Angeles Times or the Wall Street Journal is 60%.