Question

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.

Answer 1

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