(2) Suppose Tom is sitting in his office during office hours, and no students ha
ID: 3046161 • Letter: #
Question
(2) Suppose Tom is sitting in his office during office hours, and no students have come for help with their homework. Tom is bored, so he decides to play wastepaper basketball. Assume he is a somewhat poor wastepaper free throw shooter (25% success rate). Also assume his shots are independent of each other.
If he decides to shoot consecutive free throws until he makes the first one, what is the probability that this will take more than 5 attempts?
Suppose that after he makes his first shot, he shoots exactly 5 more shots. What is the probability that, out of these 5 attempts, he makes an even number of shots?
Explanation / Answer
If he decides to shoot consecutive free throws until he makes the first one, what is the probability that this will take more than 5 attempts?
Required probability = P( no success in first 5 attempts+ 6 attempts+...) = 0.75^5 *0.25+0.75^6*0.25+0.75^7*0.25+.....=0.75^5 * 0.25 *4= 0.2373
b) P( 2 shotsmade /5 shots) = 5C2 * 0.25^2 *0.75^3=10* 0.25^2 *0.75^3=0.2637
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