For a certain type of cellphone 031 of them will require a n

For a certain type of cellphone, 0.31 of them will require a new battery after a year of usage. A sample of 21 of these type of cellphones is studied. What is the probability that exactly 4 of them will require a new battery after a year of usage? Write only a number as your answer. Round to 4 decimal places (for example 0.2416). Do not write as a percentage.

Solution

Given X follows Binomial distribution with n=21 and p=0.31

P(X=x)=21Cx*(0.31^x)*((1-0.31)^(21-x)) for x=0,1,2,...,21

So the probability is

P(X=4) =21C4*(0.31^4)*((1-0.31)^(21-4)) =0.1007