# Math Help - Probability

1. ## Probability

A certain basketball team has 12 players on the roster. Each player has a 90% chance of showing up to practice, and the event that each player shows up is independent of the events that the other players do.

1. Find the number of players that are expected to attend each practice.

2. Find the probability of all 12 players showing up to practice.

3. Find the probability that fewer than 10 players show up.

2. ## Re: Probability

This is a binomial distribution with n=12 and p=0.9 Expected value =np P(X=r)=nCr(1-p)^n-r(p)^r
So P(X=12)=(0.9)^12
For fewer than 10 work out P(X=10)+P(X=11)+P(X=12) and subtract this answer from 1

3. ## Re: Probability

This looks binomial to me.

Let X be the numbers of players attending training. You have n=12 & p=0.9

1. Expected value $= n\times p$

2. $\displaystyle P(X=k) = \binom{n}{k} p^k\times (1-p)^{n-k}$ you need to find $P(X=12)$

3. Two ways to do this one, using the formula from quesiton '2'

$P(X<10) = P(X=0)+P(X=1)+P(X=2)+\cdots +P(X=9)$

or $P(X<10) = 1 - P(X=10)-P(X=11)- P(X=12)$