As a business strategy, 20 % of the new internet service subscribers selected randomly receive a special promotion. If a group of 5 such subscribers signs for the service, then the probability that at least two of them get the special promotion is

Question

As a business strategy, 20 % of the new internet service subscribers selected randomly receive a special promotion. If a group of 5 such subscribers signs for the service, then the probability that at least two of them get the special promotion is, 819 3125, 821 3125, 823 3125, 817 3125

MARKS App · Accepted Answer

Consider Binomial probability distribution. Probability of success ( p ) = 20 100 = 1 5 Probability of failure ( q ) = 1 - 1 5 = 4 5 Now, P ( r ≥ 2 ) = P ( r = 2 ) + P ( r = 3 ) + P ( r = 4 ) + P ( r = 5 ) = 5 C 2 1 5 2 4 5 3 + 5 C 3 1 5 3 4 5 2 + 5 C 4 1 5 4 4 5 1 + 5 C 5 1 5 5 4 5 0 = 1 5 5 ( 640 + 160 + 20 + 1 ) = 821 3125

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