How do we solve this?

Question

According to a survey, 60% of people have a dog. If 5 people are selected randomly, what is the probability that at least 2 of them have a dog? Round the answer to the nearest tenth of the percent.

Answer 1

This is an application of Binomial Distribution.

The expansion of (S+F)⁵ represents all possible ways for 5 'Bernoulli' trial outcomes, where S = probability of success (0.6 in this case) and F=probability of failure (1-S).

 

The answer will be the sum of all terms of the binomial expansion where exponent of S is 2, 3, 4 or 5.

Each term will be of the form nCr•P^r•F^n-r where r runs from 2 up through 5 and n=5.

The coefficients are obtained from the formula for nCr, or from the "5 row" of Pascal's triangle.

 

Can you do this calculation now?