Question

Reading the paper In a large business hotel, $40\%$of guests read the Los Angeles Times. Only read the Wall Street Journal. Five percent of guests read both papers. Suppose we select a hotel guest at random and record which of the two papers the person reads, if either. What’s the probability that the person reads the Los Angeles Times or the Wall Street Journal?

Short answer

$60$percent of the time, the person will read one of the two newspapers.

Step-by-step solution

Given Information

We have to determine probability that the person reads the Los Angeles Times or the Wall Street Journal .

Simplification

The Los Angeles Times is read by $40\%$of the guests.

The Wall Street Journal is read by $25\%$of the guests.

Only $5\%$of the visitors read both newspapers.

If there are two events, rule of thumb for addition:

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

Now,

The person's likelihood of reading the Los Angeles Times,

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

Probability that the person reads Wall Street Journal ,

  role="math" localid="1654013332190" $P\left(WSJ\right)=25\%=0.25$

Probability that the person reads both the newspapers,

  $P(LAT\cap WSJ)=5\%=0.05$

Then,

$$\begin{gathered} P(LAT\cup WSJ)=P\left(LAT\right)+P\left(WSJ\right)-P(LAT\cap WSJ)\hspace{1em} \\ P(LAT\cup WSJ)=0.40+0.25-0.05\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=0.60\hspace{0.17em} \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=60\% \end{gathered}$$

Therefore,

There is a $60\%$chance that the person reads the Los Angeles Times or the Wall Street Journal.