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

Expected Value - is the probability of an event multiplied by the amount of times the event. Therefore,

E(x) = ∑XP(X) and we know that E(x)=4.2

Let's consider

P(X=4)= f and P(X=5)= g

f+g=1 as the sum of the probabilities of all possibilities must equal 1

E=4f + 5g= 4.2 (1)

f +g= 1 (2)

f=1-g - Replacing in equation 2, we have

`\begin{gathered} 4\cdot(1-g)+5g=4.2 \\ 4-4g+5g=4.2 \\ g=0.2 \end{gathered}`

Answer: P(X=5) = 0.2