# Thread: probability with percent given.

1. ## probability with percent given.

a manufacturing plant makes dishes that are carefully inspected for the right dimensions, quality, and product trends. after studies the factory does produce 15% defectives. most of these pieces are found through inspection and redone or thrown away. Suppose two pieces are randomly selected for inspection.

what is the probablity that both pieces are defect free?

what is the probablity that neither piece is defect free?

also, if at least one of the pieces has a flaw . what is the probability that both are defective?

thanks for any help with this problem.

2. You should consider the binomial theorem

Where n is number of trials, p is the probabilty of success and k is the required amount.

$\displaystyle P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$

In your case $\displaystyle n = 2$ and $\displaystyle p = 1-0.15 = 0.85$

Originally Posted by rcmango
what is the probablity that both pieces are defect free?

Choose k = 2

Originally Posted by rcmango

what is the probablity that neither piece is defect free?

Choose k = 0

Originally Posted by rcmango
also, if at least one of the pieces has a flaw . what is the probability that both are defective?
make $\displaystyle p = 0.15$ and find $\displaystyle k=1,2$ i.e $\displaystyle P(k=1)+P(k=2)$

3. thankyou btw.