Question

A basketball player nets the ball nine times out of every ten. Let the random variable X denote the number of times the basketball player fails to net the ball before the first netting.

a) Write down the p.m.f of X

b) Find the probability that the player takes 5 trials to net the ball

Answer 1

a) $X\sim Geo(p)$

$f(x)=p(1-p)^{x}, x=0, 1, 2, ...$

Given $p=0.9$

$f(x)=0.9(1-0.9)^{x}, x=0, 1, 2, ...$

b)

$P(X=4)=0.9(1-0.9)^4=0.00009$