The outcome X of an experiment has only two possible values, X = 4 and X = 5. Given that the expected outcome E (X) = 4.2, find P (X = 5). Give your answer as a decimal.

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