16. At a carnival target game, you can keep taking shots until you miss. Each hi

Question

16. At a carnival target game, you can keep taking shots until you miss. Each hit adds one point to your score. When you miss, the game ends. Suppose your accuracy is 78% (for any particular shot, independently of other shots).
a. Identify a suitable random variable and its distribution.

b. What is the probability that in one game your score will be 5?

c. What is the probability that in one game your score is at least 4?

d. What is the probability that in one game you do not score higher than 3?

e. What is the expected value of your score?

Explanation / Answer

here it is geometric distribution wirh p=1-0.78=0.22 as game ended when you miss

b)probability that in one game your score will be 5=P(you hit 5 and on sixth you miss) =0.785*0.22=0.0635

c) probability that in one game your score is at least 4 =P(You hit 4 consecutive) =0.784=0.3702

d)  probability that in one game you do not score higher than 3 =1-P(you score at least 4)=1-0.3702=0.6298

e) expected value of score =expected number of shots-1=(1/p-1)=1/0.22 -1=3.5455

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