Consider 3 trials, each having the same probability of successes. let x denote the total number of successes in these trials.

if e(x) = 1.8, determine:

a. the largest possible value of p{x=3}?
b. the smallest possible value of p{x=3}?

in both cases, construct a probability scenario that results in p{x=3} having the stated value.

Since each trial has the same probability of success, 

Let, Xi=1 if the ith trial is a success (0 otherwise). Then, X=∑3i=1XiX=∑i=13Xi, 

and E[X]=E[∑3i=1Xi]=∑3i=1E[Xi]=∑3i=1p=3p=1.8E[X]=E[∑i=13Xi]=∑i=13E[Xi]=∑i=13p=3p=1.8

So, p=0.6p=0.6, and P{X=3}=0.63P{X=3}=0.63

I thought what I did was sound, but the textbook says the answer to (a) is 0.60.6 and (b) is 00.

Their reasoning (for (a)) is as follows:

b

step-by-step explanation: