Question

The probability that a house in an urban area will develop a leak is 6​%.If 44 houses are randomly​ selected, what is the probability that none of the houses will develop a​ leak? Round to the nearest thousandth.

Answer 1

The probability that a house in an urban area will develop a leak = p =0.06

n = number of houses = 44

Define random variable X : Number of houses in an urban area which develop a leak

X follows Binomial distribution with n = 44 and p = 0.06

If X follows Binomial distribution with n and p then

             x = 0,1,2,..........,n

Where

                           n! = 1 * 2 * 3*............*n

Here we have to find P(X = 0)

                                 0! = 1

                     

                      = 0.066           (Round to 4 nearest thousandth)

The probability that none of the houses will develop a​ leak is 0.0657