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Chapter 6: Q. 99 (page 406)

Roulette Marti decides to keep placing a 1bet on number 15in consecutive spins of a roulette wheel until she wins. On any spin, there's a 1-in- 38chance that the ball will land in the 15slot.

(a) How many spins do you expect it to take until Marti wins? Justify your answer.

(b) Would you be surprised if Marti won in 3or fewer spins? Compute an appropriate probability to support your answer.

Short Answer

Expert verified

a. The spins it take until Marti wins is 38.

b. No, its not surprised if Marti won in 3or fewer spins.

Step by step solution

01

Part (a) Step 1: Given Information

Number of consecutive spins=15

Number of chances =1in38

Number of slots=15

02

Part (a) Step 2: Explanation 

Given:

p=138

Probability (or mean) of a geometric variable is the reciprocal of the expected number:

=11/38

Hence, the number of spin will be38.

03

Part (b) Step 1: Given Information

Number of consecutive spins=15

Number of chances =1in 38

Number of slots=15

04

Part (b) Step 2: Explanation

Given:

p=138

Geometric probability formulae:

P(X=k)=qk-1p=(1-p)k-1p

Add the corresponding probabilities:

P(X鈮�3)=P(X=1)+P(X=2)+P(X=3)

鈮�0.0769

=7.69%

Because the probability is over 5%, it is not uncommon to win a prize in 3or fewer spins, so the result is not unexpected.

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