Answer:
P(X=5) = 0.2
Step-by-step explanation:
Expected outcome, E(x) = ∑XP(X)
∑ = Summation
X = outcomes
P(X) = probability of an outcome
E(X) = (4*P(X=4)) + (5*P(X=5)) = 4.2
So, 4P(X=4) + 5P(X=5) = 4.2 ... equation 1
But the sum of probabilities = 1
That is, P(X=4) + P(X=5) = 1 ... equation 2
Thus, we have the following system of equations
4P(X=4) + 5P(X=5) = 4.2 ... equation 1
P(X=4) + P(X=5) = 1 ... equation 2
Multiply equation 2 by 4
4*P(X=4) + 4*P(X=5) = 4*1
4P(X=4) + 4P(X=5) = 4 ... equation 3
4P(X=4) + 5P(X=5) = 4.2 ... equation 1
4P(X=4) + 4P(X=5) = 4 ... equation 3
Subtract equation 3 from 1
4P(X=4) - 4P(X=4) + 5P(X=5) - 4P(X=5) = 4.2 - 4
P(X=5) = 0.2
