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Chapter 6: Q. 6.7 (page 435)

In the Japanese game show Sushi Roulette, the contestant spins a large wheel that鈥檚 divided into 12 equal sections. Nine of the sections show a sushi roll, and three have a 鈥渨asabi bomb.鈥� When the wheel stops, the contestant must eat whatever food applies to that section. Then the game show host replaces the item of food on the wheel. To win the game, the contestant must eat one wasabi bomb. Find the probability that it takes 3 or fewer spins for the contestant to get a wasabi bomb

Short Answer

Expert verified

Thus, the required Probability,

P(X鈮�3)鈮�0.6836

Step by step solution

01

Given information

The Probability of success is,

p=312=14=0.25
02

Calculation

The distribution will be geometric because the variable is the number of spins required till first success.

The definition of geometric probability is as follows:

P(X=k)=qk-1脳p=(1-p)k-1脳p

To calculate the likelihood, apply the complement rule.

P(X鈮�3)=P(X=1)+P(X=2)+P(X=3)=(1-0.25)1-1(0.25)+(1-0.25)2-1(0.25)+(1-0.25)3-1(0.25)=0.25+0.75(0.25)+(0.75)2(0.25)鈮�0.6836=68.36%

As a result, there is a68.36 percent chance that the contestant will get a wasabi bomb in three or fewer spins.

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Most popular questions from this chapter

Ladies Home Journal magazine reported that 66% of all dog owners greet their dog before greeting their spouse or children when they return home at the end of the workday. Assume that this claim is true. Suppose 12 dog owners are selected at random. Let X= the number of owners who greet their dogs first.

a. Explain why it is reasonable to use the binomial distribution for probability calculations involving X.

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c. In fact, only 4 of the owners in the sample greeted their dogs first. Does this give convincing evidence against the Ladies Home Journal claim? Calculate P(X鈮�4) and use the result to support your answer.

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Researchers at the University of Michigan designed a study to find out. The researchers gave 22 students five different Hershey's Kisses (milk chocolate, dark chocolate, cr猫me, caramel, and almond) in random order and asked the student to rate each one. Participants were not told how many Kisses they would be tasting. However, when the 5th and final Kiss was presented, participants were told that it would be their last one. 9炉Assume that the participants in the study don't have a special preference for the last thing they taste. That is, assume that the probability a person would prefer the last Kiss tasted is p=0.20.

a. Find the probability that 14 or more students would prefer the last Kiss tasted.

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