Question

In a valid probability distribution, each probability must be between 0 and 1,inclusive, and the probabilities must add up to 1. If a probability distribution is1/10 1/5 1/2 x what is the value of x?

Answer 1

All probabilities must add up to 1, thus;

`(1)/(10)+(1)/(5)+(1)/(2)+x=1`

Solving, we have;

`\begin{gathered} (1)/(10)+(2)/(10)+(5)/(10)+x=1 \\ (8)/(10)+x=1 \\ x=1-(8)/(10) \\ x=(2)/(10)=(1)/(5) \\ \end{gathered}`

Thus, the answer is 1/5