You play a game where you roll a single die. You pay $1 to play, and the payouts are $0.50 if you roll an even number, $2 if you roll a 1, and $1 if you roll a 3 or 5. What are the odds for winning money if you play this game? Show your work and Explain.

Let W be the random variable representing your winnings from playing the game. Then

In short, you have a 1/6 chance of profiting from the game, and a 5/6 chance of losing money. So the odds of winning are (1/6)/(5/6) = 1/5 or 1 to 5.

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb