# 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)

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

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: $P(X\geq 2)=1-P(X\leq 1)=1-P(X=1)-P(X=0)$.