Question

In a fund-raising game for your school, you bet $1 to roll two dice. If your total is 8,9,10 or 11 you win $2. If your total is 12, you win $6. If your total is 7 or less, you lose the dollar you bet. How much, on average do you expect to win or lose with each dollar bet?

A. You will lose 56 cents
B. You will 5.6 cents.
C. On average, you will break even.
D. You will win 2/36
E. You will lose 5.6 cents

Answer 1

Answer: E , You will lose 5.6 cents

Explanation:

Because with two dice, there are 36 possible outcomes, 21 are 7 or less, 14 are 8 through 11, and 1 is twelve.

Also when you have a total of 8,9,10 or 11, you gain $1 deducing the $1 you bet. The same with when you have 12 you gain $5.

Average $ to gain when total is 8,9,10 or 11 = P(8,9,10,11)

P(8,9,10,11) = ($2-$1)(14/36) = $14/36 gain

P(12) = ($6-$1)(1/36) = $5/36 gain

P(7 or less) = (0-$1)(21/36) = -$21/36 loss

P(loss or gain)= P(8,9,10,11) + P(12) + P(7 or less)

P(loss or gain) = $( 14/36 + 5/36 - 21/36) = -$2/36

P(loss or gain) = -$0.056 = -5.6 cents loss

Therefore, For every $1 bet you will lose 5.6 cents.