If a gambler rolls two dice amd gets the sum of 5 he wins $30. If he gets a sum of 3 he wins $50. The cost of playing is $15. What is the expectation of this game? A. $0.83 B. - $3.89 C. - $8.89 D. - $12.50

C) - $8.89

Step-by-step explanation:

If he rolls two dice and gets the sum of 5, he wins $30.

If he gets the sum of 3, he wins $50

While rolling two dice, there are 36 possible outcomes (6^2) = 36

There are four possible ways (1,4 3,2 2,3 4,1) of obtaining the sum of 5 out of 36 possible outcomes.

The probability of expecting the sum of 5 = 4/36

= 1/9

This means that on every try we expect $30/9

There are two possible ways (1,2 2 2,1) of obtaining the sum of 3 out of 36 possible outcomes.

The probability of expecting the sum of 5 = 2/36

= 1/18

This means that on every try we expect $50/18

For every 9 rolls, you expect to get $30 and on every 18, you expect to get $50. On any particular roll, you should expect to gey

$30/9 + $50/18

= (60+50) / 18

= 110/18

= $6.11

Given that each game he is playing cost $15. The overall expectations is to lose (15 - 6.11) = $8.89 each time he plays.

Answer = - $8.89