Supopose that an ethernet card manufacturer knows from experience than on averag

Question

Supopose that an ethernet card manufacturer knows from experience than on average one out of forty cards has a particular defect. a) out of the next 4 cards manufactured, what is the probability that atleast one of them will have this defect? b)suppose the company begins monitoring their manufactured cards at the beginning of a production run what is the probability that the first card to have this defect is the seventh to be monitored? explain with binomial distribution and geometric distribution.

Explanation / Answer

a) This will be a binomial experiment with parameters:

n = 4, p = 1/40 = 0.025

q = 1 - p = 1 - 0.025 = 0.975

Hence,

P(At least one defective)

= 1 - P(None defective)

= 1 - (0.975)4

= 0.0963 [Rounded off to 4 decimal places]

b) P(First defective will be the 7th monitored)

= P(First six not defective)*P(7th defective)

= (0.975))6 * (0.025)

=0.0215   [Rounded off to 4 decimal places]

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