Question

Here’s my dilemma, I can accept a $1000 bill or play a game ten times. For each roll of the single die, I win $500 for rolling 1 or 2, I win $400 for rolling 3; and I lose $300 for rolling 4,5,or 6. Based on the expected value, I should accept the $1000 bill.

Answer 1

you should accept the $1,000 bill

Explanation:

Given the information:

• $500 for rolling 1 or 2
• $400 for rolling 3
• lose $300 for rolling 4,5,6

P (rolling 1 or 2) = 1/6 + 1/6 = 2/6 = 1/3

P (rolling a 3) = 1/6

P (rolling 4 or 5 or 6) = 3/6 = 1/2

Hence, the expected value for 1 time is:

E = (1/3)*500 + (1/6)*400 - (1/2)*300

E = $166 + $66 - $150

E = $82

Expected value is linear so if you roll the die 10 times, expected value is: 10*82 = $820

The expected value is $82, meaning you should accept the $1,000 bill