Question

If a gambler rolls two dice and gets the sum of 7, he wins $20. If he gets a sum of 4, he wins $40. The cost of playing is $14. What is the expectation of this game?

Answer 1

The expectation is that he should be losing money because the chances he rolls either a 7 or a 4 out of 2 dice (which is 1-12) is 1/6. I think this is what you're trying to ask I hope I helped

Answer 2

The expectation of this game is -$7.33

Further explanation

The probability of an event is defined as the possibility of an event occurring against sample space.

Let us tackle the problem.

If a gambler rolls two dice and gets the sum of 7 , there are 6 ways to get the sum of 7 , i.e : ( 1,6 ) , ( 2,5 ) , ( 3,4 ) , ( 4,3 ) , ( 5,2 ) , ( 6,1 ) from total 36 sample spaces, then the probability is :

$P(7) = \frac{6}{36}$

$\large {\boxed {P(7) = \frac{1}{6} } }$

If a gambler rolls two dice and gets the sum of 4 , there are 3 ways to get the sum of 4 , i.e : ( 1,3 ) , ( 2,2 ) , ( 3,1 ) from total 36 sample spaces, then the probability is :

$P(4) = \frac{3}{36}$

$\large {\boxed {P(4) = \frac{1}{12}} }$

Because the gambler wins $20 when he gets the sum of 7 , and wins $40 when he gets a sum of 4 , then :

$Expectation ~ = ~ Winning ~ - ~ Cost$

$Expectation ~ = ~ ( \ 20 \times \frac{1}{6} + \ 40 \times \frac{1}{12}) ~ - ~ \ 14$

$Expectation ~ = ~ ( \ 20 \div 3 ) - \ 14$

$Expectation ~ = ~ ( \ 6.67 ) - \ 14$

$\large {\boxed {Expectation ~ = ~ -\ 7.33} }$

Learn more

• Different Birthdays : brainly.com/question/7567074
• Dependent or Independent Events : brainly.com/question/12029535
• Mutually exclusive : brainly.com/question/3464581

Answer details

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die