Problem 8. Suppose that you have a revolver that holds up to five bullets. Suppose that exactly one bullet is loaded. You spin the cylinder and then pull the trigger. You repeat this process until the gun fires. a. What is the probability that the gun fires on the fourth trial? b. What is the probability that it fires before the fourth trial? c. What is the probability that it fires after the third trial?

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Problem 8. Suppose that you have a revolver that holds up to five bullets. Suppose that
exactly one bullet is loaded. You spin the cylinder and then pull the trigger. You repeat
this process until the gun fires.
a. What is the probability that the gun fires on the fourth trial?
b. What is the probability that it fires before the fourth trial?
c. What is the probability that it fires after the third trial?
d. What is the probability that it fires on the seventh trial given that it does not fire in
the first five trials?
e. What is the probability that it fires on the fifth trial given that it fires on an odd trial?
f. What is the expected number of trials?
Transcribed Image Text:Problem 8. Suppose that you have a revolver that holds up to five bullets. Suppose that exactly one bullet is loaded. You spin the cylinder and then pull the trigger. You repeat this process until the gun fires. a. What is the probability that the gun fires on the fourth trial? b. What is the probability that it fires before the fourth trial? c. What is the probability that it fires after the third trial? d. What is the probability that it fires on the seventh trial given that it does not fire in the first five trials? e. What is the probability that it fires on the fifth trial given that it fires on an odd trial? f. What is the expected number of trials?
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