Question

You play a game where you toss a die. If the die lands on a 6, you win $6. It costs $2 toplay. Construct a probability distribution for your earnings. Find your expected earnings.

Answer 1

Now from the question, if the die lands on 6, I win $6. So probability of landing on 6 is

`(1)/(6)\text{ since a die has 6 faces }`

Since I will pay $2 to play, we subtract this from $6 that we will win.

And probability of losing becomes

`(5)/(6)\text{ }`

The table becomes

From the table the expected earnings is calculated as

`\begin{gathered} E=\sum_^xP(x) \\ =4((1)/(6))-2((5)/(6)) \\ =(4)/(6)-(10)/(6) \\ =-(6)/(6) \\ =-1 \end{gathered}`

Hence expected earnings is -$1