A door-to-door encyclopedia salesperson is required todocument five in-home visi

Question

A door-to-door encyclopedia salesperson is required todocument five in-home visits each day.Suppose that she has a 30%chance of being invited into any given home, with each addressrepresenting an independent trial. What is the probability that sherequires fewer than eight houses to achieve her fifthsuccess? (The answer is 0.029, how can I get this answer?) A door-to-door encyclopedia salesperson is required todocument five in-home visits each day.Suppose that she has a 30%chance of being invited into any given home, with each addressrepresenting an independent trial. What is the probability that sherequires fewer than eight houses to achieve her fifthsuccess? (The answer is 0.029, how can I get this answer?)

Explanation / Answer

This is a negative binomial question, since you are looking for therth (5th) success in a series of bernoulli triials. Let X = the number of visits to a house in order to have fivesuccesses. Then, X is Negative Binomial with r = 5, p = 0.3 P( X < 8) = P(X = 5) + P(X = 6) + P(X=7), since you can't have less visitsthan the number of successes = 4C4*(0.3)5(0.7)0 +5C4*(0.3)5(0.7)1 +6C4*(0.3)5(0.7)2 = 0.0287955

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