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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鈥檚 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 PLCW.

Short Answer

Expert verified

(a) The Venn diagram is

.

(b) The value of PLCWis0.20.

Step by step solution

01

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.

02

Part (a) Step 2: Explanation

According to the question,

The probability of a guest reading the Los Angeles Times is0.40, probability of a guest reading Wall Street journals is0.25, and those who have both is0.05.

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

03

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 ofPLCW.

04

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 Times1-0.40=0.60, which is, and the probability of a guest reading the Wall Street Journal0.25, which is, and the probability of a guest reading not the Los Angeles Times but Wall Street is0.25+0.40=0.65.

Now, apply the union rule of probability,

which isPAB=P(A)+P(B)+P(AB)

We getPLCW=0.60+0.25-0.65=0.20.

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