Question

A company markets educational software products and is ready to place three new products on the market. Past experiences has shown that for this particular software, the chance of "success" is 80%. assume that the probability of success is independent for each product.

find the probability that exactly 1 of the 3 products is successful.

(please try to show step by step)

Answer 1

Applying the binomial probability formula,

P(x) = (nCx) * (p^x) * [ q^ (n-x)] where C is the combination

In the given problem, n= 3, x = 1, p = 80% or 0.8 , q = 1-p = 1-0.8 = 0.2

Which means,

P(1) = (3C1) * (0.8 ^ 1) * (0.2^ (3-1)) = (3C1) * 0.8 * (0.2^2) = [3! / 1! * (3-1) !] * 0.8 * 0.2 * 0.2

P(1) = 3 * 0.8 * 0.2*0.2 = 0.096

NOTE: Similarly, we can check in the binomial probability table, considering = 0.8, n=3 which is a sample size and x=1