Question

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

The correct option is (c) $8/36$

Step-by-step solution

Step 1. Given Information

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

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.

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

$$\begin{gathered} P(AorB)=P(A\cup B) \\ P(AorB)=P\left(A\right)+P\left(B\right)-P(A\cap B) \end{gathered}$$

If events A and B are mutually exclusive,

Then

$$\begin{gathered} P(A\cap B)=0 \\ P(7or11)=P\left(A\right)+P\left(B\right) \\ P(7or11)=\frac{8}{36} \end{gathered}$$

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