# Math Help - Theortical Probability

1. ## Theortical Probability

A food inspector at a grocery store discovers that 25%(or1/4) of all of the apples from the store have worms. Mou, a shopper, buys 6 apples. What's the probability that none of the six apples he buys have no worms?

18/24 no worms? Sounds too easy.

2. ## Re: Theortical Probability

Let X be a random variable representing an apple having a worm and follows a binomial distribution.

Call p the probability of an apple having a worm, p=0.25 and n=6. Therefore X is Bi(6,0.25)

Find the probability that X=0. i.e. P(X=0) can be found using the following

$P(X=k) = ^nC_k\times p^k\times (1-p)^{n-k}$

3. ## Re: Theortical Probability

Originally Posted by terminator
A food inspector at a grocery store discovers that 25%(or1/4) of all of the apples from the store have worms. Mou, a shopper, buys 6 apples. What's the probability that none of the six apples he buys have no worms?
Assuming that all events are independent with probability 0.25 the answer is $\binom{6}{0}(0.25)^0(1-0.25)^{6-0}$.