Question

A game is played in which three dice are rolled, and the number of “1”s that appear is recorded.
a) Determine the probability distribution for the random variable X, the number of “1”s in three rolls.
b) Suppose you win $1 if a “1” appears once, you win $2 if a “1” appears twice, and you win $3 if a “1” appears three times. However, if there are no “1”s rolled, then you lose $1. Calculate your expected winnings/losses from playing this game.

c) Is this game “fair”? Explain.

Answer 1

for part a:

Zero "1" : (5/6)^3 = 125/216
One "1" : (3)(1/6)(5/6)^2 = 25/72
Two "1" : (3)(5/6)(1/6)^2 = 5/72
Three "1" : (1/6)^3 = 1/216

Answer 2

thnx n b?

Answer 3

(-1)(125/216) + (1)(25/72) + (2)(5/72) + (3)(1/216) is your expected win/loss.

For part c: if the above is not "0", it is not a fair game. It would then be either in your favor or the other person's.

Answer 4

thnx so much for ur helping!

Answer 5

You're welcome!

Answer 6

-0.578+0.347+0.1389+0.0014=-0.0782

Answer 7

-0.0782

Answer 8

Yes. and since this is not zero, it is not a fair game. This game actually goes against you. If you played this for a long time, you would eventually lose all of your money. Just like the casino games.

Answer 9

thnx so much

Answer 10

You're welcome.

Answer 11

Are you all set now? @hager

Answer 12

ya thnx

Answer 13

Good luck in all of your studies and thx for the recognition! @hager

Answer 14

thnx u thnx for helping me