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Chapter 5: Q 60. (page 311)

The casino game craps is based on rolling two dice. Here is the assignment of probabilities to the sum of the numbers on the up-faces when two dice are rolled: pass line bettor wins immediately if either a 7 or an 11 comes up on the first roll. This is called a natural. What is the probability of a natural?

(a) 2/36 (c) 8/36 (e)20/36

(b) 6/36 (d) 12/36

Short Answer

Expert verified

The correct option is (c) 8/36

Step by step solution

01

Step 1. Given Information

When two dice are rolled, probabilities are assigned to the total of the numbers on the up-faces.

02

Step 2. Concept Used

Definition of the probability addition theorem: Assume A and B are two events in a random experiment, and you want to know whether A or B has a higher likelihood. Then apply the probability addition theorem.

03

Step 3. Calculation

Assume A and B are two events in a random experiment, and you want to know whether A or B has a higher probability. Then apply the probability addition theorem.

That is

P(AorB)=P(A鈭�B)P(AorB)=P(A)+P(B)鈭�P(A鈭�B)

If events A and B are mutually exclusive,

Then

P(A鈭�B)=0P(7or11)=P(A)+P(B)P(7or11)=836

Therefore, The probability of P (7 or 11)=8/36

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Most popular questions from this chapter

Who eats breakfast? Refer to Exercise 49.

(a) Construct a Venn diagram that models the chance process using events B: eats breakfast regularly, and M: is male.

(b) Find P(B鈭�M) Interpret this value in context.

(c) Find P(Bc鈭�Mc) Interpret this value in context.

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.

Explain why events A and B are mutually exclusive

Keep on tossing The figure below shows the results of two different sets of 5000coin tosses. Explain what this graph says about chance behavior in the short run and the long run.

Find the probability that the computer is a laptop. Show your work.
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