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What is the probability that he will sell a car to exactly 2 of the next 3 customers?

A new car salesperson knows that he sells cars to one customer out of 20 who enter the showroom. What is the probability that he will sell a car to exactly 2 of the next 3 customers?

Public Comments

1. 3C2 * .05^2 * .95^1 = .007125
2. Let X be the number of cars sold. X has the binomial distribution with n = 3 trials and success probability p = 0.05 In general, if X has the binomial distribution with n trials and a success probability of p then P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x) for values of x = 0, 1, 2, ..., n P[X = x] = 0 for any other value of x. The probability mass function is derived by looking at the number of combination of x objects chosen from n objects and then a total of x success and n - x failures. Or, in other words, the binomial is the sum of n independent and identically distributed Bernoulli trials. X ~ Binomial( n , p ) the mean of the binomial distribution is n * p = 0.15 the variance of the binomial distribution is n * p * (1 - p) = 0.1425 the standard deviation is the square root of the variance = √ ( n * p * (1 - p)) = 0.3774917 The Probability Mass Function, PMF, f(X) = P(X = x) is: P( X = 0 ) = 0.857375 P( X = 1 ) = 0.135375 P( X = 2 ) = 0.007125 ← answer P( X = 3 ) = 0.000125