Finding the possible values for probabilities?

Question

Consider 3 trials, each having the same probability of success. Let X denote the total number of successes in these trials. If E[X} = 0.6, find each of the following.

(a) The largest possible value of P{X=3}: (already solved) P{x=3} <= 0.2

(b) The smallest possible value of P{X=3}: (already solved) P{x=3} >= 0

In this case, give possible values for the remaining probabilities:
P{X=0} =
P{X=1} =
P{X=2} =

I ve tried 0, 0.1, 0.2, and 0.6.

I have the equation for expected values, but I m unsure about the possible values in the last section. Any help is appreciated!

Answer 1

I am not sure why the questions have been phrased as they have been.

 

What you are talking about here is the binomial distribution with n = 3 and p = .2, i.e. E(X) = 3*.2 = .6

 

The probabilities are as follows

P(X = 0) = .512, P(X = 1) = .384, P(X = 2) = .0960 and P(X = 3) = .008.