Question

Playing game of chance and pay 300 by rolling a fair die one time if you rome a 2 and receive $1300 if you roll a 4 or six you receive $900 if you ore a 3 5 or 9 receive nothing. find expected value for this game. based on value is it a good game to play?

Answer 1

Possible typo in bold:
"Playing game of chance and pay 300 by rolling a fair die one time if you rome a 2 and receive $1300 if you roll a 4 or six you receive $900 if you ore a 3 5 or <b>one</b> receive nothing. find expected value for this game. based on value is it a good game to play?"

If x and P(x) represents the winning amount and P(x) the probability for a particular outcome, then
ΣxP(x) represents the expected value of the game, i.e. expected amount of winnings averaged over a large number of trials.

Outcome x P(x) xP(x)
1 -300 1/6 -50
2 1300-300 1/6 166.67
3 -300 1/6 -50
4 900-300 1/6 100
5 -300 1/6 -50
6 900-300 1/6 100
ΣxP(x)=-50+200-50+100-50+100=216.67
The expected value (winning) is $216.67