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Chapter 5: Q R5.4. (page 334)

Weird dice Nonstandard dice can produce interesting distributions of outcomes. Suppose you have two balanced, six-sided dice. Die A has faces with 2,2,2,2,6, and6 spots. Die B has three faces with 5 spots and three faces with 1 spot. Imagine that you roll both dice at the same time.

(a) Find a probability model for the difference (Die A 鈭� Die B) in the total number of spots on the up-faces.

(b) Which die is more likely to roll a higher number? Justify your answer.

  • Use basic probability rules, including the complement rule and the addition rule for mutually exclusive events.

Short Answer

Expert verified

Part (a) Probability distribution isDProbability-313112516

Part (b) Die A can take higher values in comparison of the die B.

Step by step solution

01

Part (a) Step 1. Given Information

Die A takes the values2 and 6, whereas Die B takes the values 5 and 1

02

Part (a) Step 2. Concept

Probability=FavorableoutcomesTotaloutcomes

03

Part (a) Step 3. Calculation

The difference can be determined using the following formula:

2鈭�5=鈭�32鈭�1=6鈭�5=16鈭�1=5

The probabilities could be estimated in the following way:

P(2,5)=46脳36=13P(2,1)=46脳36=13P(6,5)=26脳36=16P(6,1)=26脳36=16

As a result, the probability distribution is as follows:

DProbability-313112516

04

Part (b) Step 3. Explanation

Die A could take the values 2 and 6based on the information supplied, whereas Die B may take the values 5 and 1. As a result, it's possible to say that die A can take higher values than die B.

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Most popular questions from this chapter

Recycling Do most teens recycle? To find out, an AP Statistics class asked an SRS of 100 students at their school whether they regularly recycle. How many students in the sample would need to say 鈥淵es鈥� to provide convincing evidence that more than half of the students at the school recycle? The Fathom dot plot below shows the results of taking 200 SRSs of 100 students from a population in which the true proportion who recycle is 0.50.

(a) Suppose 55 students in the class鈥檚 sample say 鈥淵es.鈥� Explain why this result does not give convincing evidence that more than half of the school鈥檚 students recycle.

(b) Suppose 63 students in the class鈥檚 sample say 鈥淵es.鈥� Explain why this result gives strong evidence that a majority of the school鈥檚 students recycle.

Probability models? In each of the following situations, state whether or not the given assignment of probabilities to individual outcomes is legitimate, that is, satisfies the rules of probability. If not, give specific reasons for your answer.

(a) Roll a die and record the count of spots on the up-face: P(1) = 0, P(2) = 1/6, P(3) = 1/3, P(4) = 1/3,

P(5) = 1/6, P(6) = 0.

(b) Choose a college student at random and record gender and enrollment status: P(female full-time) = 0.56, P(male full-time) = 0.44, P(female part-time) = 0.24, P(male part-time) = 0.17.

(c) Deal a card from a shuffled deck: P(clubs) = 12/52, P(diamonds) = 12/52, P(hearts) = 12/52,

P(spades) = 16/52.

Who eats breakfast? Students in an urban school were curious about how many children regularly eat breakfast. They conducted a survey, asking, 鈥淒o you eat breakfast on a regular basis?鈥� All 595 students in the school responded to the survey. The resulting data are shown in the two-way table

below.7 Male Female Total Eats breakfast regularly 190110300 Doesn鈥檛 eat breakfast regularly 130165295Total320275595

(a) Who are the individuals? What variables are being measured?

(b) If we select a student from the school at random, what is the probability that we choose

  • a female?
  • someone who eats breakfast regularly?
  • a female who eats breakfast regularly?
  • a female or someone who eats breakfast

regularly?

Role-playing games Refer to Exercise 39. Define event A: sum is 5. Find P(A).

Monty Hall problem In Parade magazine, a reader posed the following question to Marilyn vos Savant and the 鈥淎sk Marilyn鈥� column: Suppose you鈥檙e on a game show, and you鈥檙e given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what鈥檚 behind the doors, opens another door, say #3, which has a

goat. He says to you, 鈥淒o you want to pick door #2?鈥� Is it to your advantage to switch your choice of doors? The game show in question was Let鈥檚 Make a Deal and the host was Monty Hall. Here鈥檚 the first part of Marilyn鈥檚 response: 鈥淵es; you should switch. The first door has a 1/3 chance of winning, but

the second door has a 2/3 chance.鈥� Thousands of readers wrote to Marilyn to disagree with her answer. But she held her ground.

(a) Use an online Let鈥檚 Make a Deal applet to perform at least 50 repetitions of the simulation. Record whether you stay or switch (try to do each about half

the time) and the outcome of each repetition.

(b) Do you agree with Marilyn or her readers? Explain.
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