A basketball player shoots free throws until he makes one. However his coach wan

Question

A basketball player shoots free throws until he makes one. However his coach wants him to practice his technique and the feel of the motions, his coach had the player blindfold himself which makes each throw independent from the others. When he is blindfolded he only has 6% chance of making a free throw on a particular try.
a) What is the probability that he will have to throw over 150 balls until he makes his first basket? (Think about what kind of distribution this is) b) What is the expected number of throws he will need to make until he makes his first basket? c) What is the standard deviation of throws he will need to make until he makes his first basket? A basketball player shoots free throws until he makes one. However his coach wants him to practice his technique and the feel of the motions, his coach had the player blindfold himself which makes each throw independent from the others. When he is blindfolded he only has 6% chance of making a free throw on a particular try.
a) What is the probability that he will have to throw over 150 balls until he makes his first basket? (Think about what kind of distribution this is) b) What is the expected number of throws he will need to make until he makes his first basket? c) What is the standard deviation of throws he will need to make until he makes his first basket?
a) What is the probability that he will have to throw over 150 balls until he makes his first basket? (Think about what kind of distribution this is) b) What is the expected number of throws he will need to make until he makes his first basket? c) What is the standard deviation of throws he will need to make until he makes his first basket?

Explanation / Answer

a) If it requires overs 150 ballls to make the first throw, the first 150 throws are all misses.

Probability = 0.94150 = 0.00009315.

b) Expected number of makes = np = 1

p = 0.06

=> n = 1 / 0.06 = 16.6667 or 17 throws.

c) Standard deviation = (np(1-p))

= (1*0.94)

= 0.94

= 0.9695.

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