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

Posted in: darrelrussell.com edit
07 Jan 2009
  • 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?


  • 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


  • 3C2 * .05^2 * .95^1 = .007125