Hi! I really need help with this problem, if you could show work so I could foll

Question

Hi! I really need help with this problem, if you could show work so I could follow along I would greatly appreciate it! Thanks in advance!

4.6 A street vendor is asking people to play a simple game. You roll a pair of dice. If the sum on the dice is 10 or higher, you win 810. If you roll a pair of 1's, you win $50. Otherwise you lose $5. If the random variable X equals your win (or loss) for each play, find = E(X) fi.e. figure out how much we expect to win or lose for each play, on average). Is it wise to play this game? Why?

Explanation / Answer

The various combinations for the two dice that yield a sum of 10 or higher are

6,6

6,5

5,6

6,4

4,6

5,5

They are 6 in number.

Total possible outcomes = 6*6 = 36

(1,1) can come in 1 way.

E(X) = $10 * 6/36 + $50 * 1/36 - $5 * 29/36

= -0.97$

Since the expected value is negative it is not wise to play the game.

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