Can you help with this homework question?

Najji is able to make sales to 20 out of every 100 potential customers at Best Buy that he sees. Yesterday he spoke with 15 people. What is the probability that he made at least two sales? Show all your work. 

Answer:

Probability = 0.8329

Step-by-step explanation

We will use the Binomial distribution for this question since we are attempting a "trial" a set amount of times and looking for a certain amount of successes.

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

n = 15 since that is the number of people he spoke to (number of "trials")

p = 20 / 100 = 0.2 (his success in making sales)

We want the probability of AT LEAST 2 sales, so 2 of more sales. Since it would take a long time to calculate from 2 to 15, we can calculate the probability of making only 0 or 1 sale, and subtract that from 1.

P(0) = C(15, 0) * (0.2)⁰ * (0.8)¹⁵

= 1 * 1 * 0.0351 = 0.0352

P(1) = C(15, 1) * (0.2)¹ * (0.8)¹⁴

= 15 * 0.2 * 0.0440 = 0.1319

Add the probabilities to get 0.1671. Subtract from 1: 1 - 0.1671 = 0.8329