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.

you should accept the $1,000 bill

Step-by-step explanation:

Given the information:

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

b

unless you made a typo, the answers are both a and c.

step-by-step explanation:

1.5/3 is .5 whereas 3/9 is .3333333 not proportional

22/33 is .66666 and 4/6 is also .66666 proportional

2/4 is .5 whereas 142/213 is .66666 not proportional

14/7 is 2 and 7/3.5 is also 2 proportional

you could've also checked it by doing this simple division:

if the larger fraction divides with the smaller fraction to equal 1, it is proportional. so let me show you what i mean:

when i divide 22/33 by 4/6 i get 1, so we know it is proportional, and it is the same with 14/7 and 7/3.5. now if i divide 3/9 by 1.5/3 i get .66666 so therefore we know it is not proportional.

there are many ways to do this so i wanted to show you some possible ways.