Question

Reading the paper In a large business hotel, 40% of guests read the Los Angeles Times. Only 25% 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?

a. Make a Venn diagram to display the outcomes of this chance process using events L:reads the Los Angeles Times and W: reads the Wall Street Journal.

b. Find P$\left(L^C\cap W\right)$.

Short answer

(a) The Venn diagram is

.

(b) The value of P$\left(L^C\cap W\right)$is$0.20$.

Step-by-step solution

Part (a) Step 1: Given Information

We are given the values of the probability of guest reading the Los Angeles Times and guest reading Wall Street Journals, and we have to make a Venn diagram to show the probability of guest reading any one of the newspapers.

Part (a) Step 2: Explanation

According to the question,

The probability of a guest reading the Los Angeles Times is$0.40$, probability of a guest reading Wall Street journals is$0.25$, and those who have both is$0.05$.

A Venn diagram shows the probability of reading any one of the newspapers.

Part (b) Step 1: Given Information

We are given the values of the probability of guest reading the Los Angeles Times and the Wall Street Journals, and we have to find out the value of$\mathrm{P}\left({\mathrm{L}}^{\mathrm{C}}\cap \mathrm{W}\right)$.

Part (b) Step 2: Explanation

To find out the value of the given probability, we required the probability of a guest not reading the Los Angeles Times$1-0.40=0.60$, which is, and the probability of a guest reading the Wall Street Journal$0.25$, which is, and the probability of a guest reading not the Los Angeles Times but Wall Street is$0.25+0.40=0.65$.

Now, apply the union rule of probability,

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

We get$P\left(L^C\cap W\right)=0.60+0.25-0.65=0.20$.