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Chapter 5: Q. 73 (page 350)

The Pew Research Center asked a random sample of 2024adult cell-phone owners from the United States their age and which type of cell phone they own: iPhone, Android, or other (including non-smartphones). The two-way table summarizes the data.

Suppose we select one of the survey respondents at random.

a. Find P(iPhone|18-34).

b. Use your answer from part (a) to help determine if the events “iPhone” and "18-34"are independent.

Short Answer

Expert verified

Part a. 0.327

Part b. iPhone & 18-34are not independent.

Step by step solution

01

Part a. Step 1. Given information

The Table is-

02

Part a. Step 2. Calculation

We have,

P(iPhone|18-34)=169517=0.327

Therefore, the solution is0.327.

03

Part b. Step 1. Calculation

We have,

P(iPhone|18-34)=P(iPhone∩18-34)P(18-34)

If iPhone & 18-34are independent

=P(iPhone|·P(18-34)P(18-34)=P(iPhone)

Now,

P(iPhone)=4672024=0.2307≠0.327

Therefore, iPhone & 18-34are not independent.

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Most popular questions from this chapter

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?

Which of the following is a correct way to perform the simulation?

a. Let integers from 1to34represent making a free throw and 35to50represent missing a free throw. Generate 50random integers from1to50. Count the number

of made free throws. Repeat this process many times.

b. Let integers from 1to34represent making a free throw and 35to50represent missing a free throw. Generate 50 random integers from 1 to 50 with no repeats

allowed. Count the number of made free throws. Repeat this process many times.

c. Let integers from1to56represent making a free throw and 57to100represent missing a free throw. Generate 50 random integers from1to100.Count the number of made free throws. Repeat this process many times.

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Is this your card? A standard deck of playing cards (with jokers removed) consists of 52 cards in four suits—clubs, diamonds, hearts, and spades. Each suit has 13 cards, with denominations ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. The jacks, queens, and kings are referred to as “face cards.” Imagine that we shuffle the deck thoroughly and deal one card. The two-way table summarizes the sample space for this chance process based on whether or not the card is a face card and whether or not the card is a heart.

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Are the events “heart” and “face card” independent? Justify your answer.
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