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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∪B)P(AorB)=P(A)+P(B)−P(A∩B)

If events A and B are mutually exclusive,

Then

P(A∩B)=0P(7or11)=P(A)+P(B)P(7or11)=836

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

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