1 An event E has a probability p PE 01 in some sample spac

1) An event E has a probability p = P(E) = 0.1 in some sample space. Suppose the experiment that yields this sample space is repeated 5 times and the outcomes are independent. Find the probability of getting E exactly 3 times. Round your answer to 6 decimal places.

2) Let X denote a random variable having a binomial distribution with n = 20 and p = 0.08.
Find the the probability that X is 2, or fewer.

Solution

1)

p=0.1

It is a binomial probability .

P(X=r) = nCr * (p)^r * (1-p)^(n-r)

P(X=3) = 5C3 * ( 0.1)^3 * ( 1-0.1)^2

= 0.0081Answer

2)

P(X=2 or fewer)

=P(X<=2)

= P(X=0) + P(X=1) +P(X=2)

=20C0 * ( 0.08)^0 * ( 1-0.08)^20 + 20C1 * ( 0.08)^1 * ( 1-0.08)^19 + 20C2 * ( 0.08)^2 * ( 1-0.08)^18

= 0.787946 Answer