Question

a realtor has 10 houses on the market and predicts that she has a 15% chance of selling each house this week. If the houses are sold independently of each other, then

A.) what are the chances of selling exactly three houses in the week?

B.) What are the chances of selling at least one house in the week?

Answer 1

n = 10

p = 0.15

It is a binomial distribution.

P(X = x) = nCx * p^x * (1 - p)^{n - x}

a) P(X = 3) = 10C3 * (0.15)^3 * (0.85)^7 = 0.12983

b) P(X > 1) = 1 - P(X < 1)

                = 1 - P(X = 0)

                = 1 - (10C0 * (0.15)^0 * (0.85)^10)

                = 1 - 0.19687

               = 0.80313