Suppose that 98% of a very large population of SIMMs are good and you randomly s

Question

Suppose that 98% of a very large population of SIMMs are good and you randomly select SIMMs one at a time, inspect each, and discard any SIMM that is not good. (a) What is the expected number of good SIMMs you have passed when you find the first bad SIMM? (b) If you have just discarded your 2nd bad SIMM, what is the expected number of good SIMMs that you have passed? (c) Given that you have inspected 20 SIMMs and found that there was 1 bad SIMM, what is the probability that the first 5 SIMMs were good?

Explanation / Answer

a) 98% SIMMs are good

So, there are 2 bad and 98 good SIMMs expected in 100

so, expected number of SIMMs passed before finding first SIMM = 98/2 = 49

b) Expected number of good SIMMs passed after before discarding the 2nd bad SIMM = 98

c) In the first 20, one is bad. P(good) = 19/20

P(first 5 SIMMs were good) = (19/20)5 = 0.7738

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