# Probability that product will be faulty

Probability that products won't pass the test is 0.01. Calculate the probability among 200 of such products - at least 2 won't pass the test.

a) Provide a formula for exact probability

there is one more point here i have no idea how to translate let me try though

Provide formula for probability of approximate distribution of a)

If that makes sense, great otherwise please help me with the first one.

Would it be:

p=0.01 n=200 EX=2

D²(X) = npq = 200*0.01*0.99 ?

Because going like:

100 choose 4 * (5/100)^4 * (95/100)^4 + 100 choose 5 * (5/100)^5 * (95/100)^5 +.....=

this would seem to be so much of an effort to calculate that even on a calculator?

• Hint: calculate the probability of the complement, i.e. that $0$ or $1$ won't pass the test. – drhab Sep 6 '15 at 18:44

## 1 Answer

Hint for a): You are on the right track. You have the expected value and the variance of the binomial distribution. Now use the cdf to provide a formula, which calculates the sum of $2$ upto $200$ successes. After that you can apply the converse probability: $P(X\geq 2)=1-P(X\leq 1)=1-P(X=1)-P(X=0)$.