Question

Suppose a computer chip manufacturer rejects 2% of the chips produced because they fail presale testing. a) What’s the probability that the fifth chip you test is the first bad one you find? b) What’s the probability you find a bad one within the first 10 you examine?

Answer 1

Answer:

a) 0.0184

b) 0.1829

Step-by-step explanation:

a) With geometric distribution you can measure the number of trials until the first success, that is, a defective chip is found, as follows:

P(x = k) = p*(1-p)^(k-1)

This means: probability to find exactly 1 defective in k trials, p is the probability to find a defective chip, which is equal to 0.02, and the number of trials are k = 5. Replacing:

P(x = 5) = 0.02*(1-0.02)^(5-1) = 0.0184

b) If you want the probability of 1 success within k trials, compute:

$P(x$

Replacing with k = 10

$P(x$