Question

The probability a car salesman sells a car to a customer is 0.05

Assuming the salesmen sees 12 customers in a week, what is the probability he sells less than 3 cars?

Answer 1

Here, n = 12, p = 0.05, (1 - p) = 0.95 and x = 3
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X < 3).
P(X < 3) = (12C0 * 0.05^0 * 0.95^12) + (12C1 * 0.05^1 * 0.95^11) + (12C2 * 0.05^2 * 0.95^10)
P(X < 3) = 0.5404 + 0.3413 + 0.0988
P(X <3) = 0.9805