Answer to Question #342789 in Statistics and Probability for Zain

Question

80% of all business startups in the IT industry report that they generate a profit in their first year. If a sample of 10 new IT business startups is selected, find the probability that exactly seven will generate a profit in their first year.

Answer 1

There are only two possible mutually exclusive outcomes – to generate a profit in the first year or not (yes or no).

There are a fixed number of trails (startups) – 10.

The IT startups are independent and it is reasonable to assume that this is true.

The probability of success for each startup is 0.8.

We know that:

n = 10, p=0.80, q=0.20, x=7

The probability of 7 IT startups to generate a profit in their first year is:

$P(x=7)=\frac{10!}{(10-7)!7!}0.8^7(1-0.8)^{10-7}=0.2013.$

So, there is a 20.13% probability that exactly 7 of 10 IT startups will generate a profit in their first year when the probability of profit in the first year for each startup is 80%.