Question

There are 3 one dollar bills and 2 five dollar bills in your left pocket and 5 one dollar bills and 1 five dollar bills in your right pocket. You pick two bills at random from the left pocket and put them in the right one. Then you randomly take two bills from your right pocket

1. Probability that you move two dollars is? (Answer: 3/10)

2. Probability that you move six dollars is? (Answer:6/10)

3. Probability that you move ten dollars is? (Answer:1/10)

4. Conditional probability that you take two dollars from the right pocket given that you moved two dollars is (Answer: 3/4)

5. Conditional probability that you take two dollars from the right pocket given that you moved six dollars is (Answer: 15/28)

6. Conditional probability that you take two dollars from the right pocket given that you moved ten dollars is? (Answer: 5/14)

Answer 1

Please don't hesitate to give a "thumbs up" for the answer in case the answer has helped you

a/

P( move $2 ) = choose any 2 of 3 $1 bills and move them / select any 2 bills from the 5 bills

= 3C2 / 5C2

= 3/10

b/

P( move $6 ) = choose a $5 and a $1 bill and move them / select any 2 bills from 5 bills

= 2C1 * 3C1 / 5C2

= 6/10

c/ P( move $10) = choose 2 $5 bills / select any 2 bills from 5 bills

= 2C2 / 5C2

= 1/10

d/ Then you have 7 $1 bills and 1 $5 bill in right .

P( take 2 $1 from right pocket) = 7C2 / 8C2 = 7*6/ 8*7 = 3/4

e/

Then you have 7 $1 bills and 1 $5 bill in right .

P( take $1 + $5 from right pocket) = 6C2  / 8C2 = 6*5/ (4*7) = 15/28

f/

P(take 2 * $5 from right pocket) = 5C2 / 8C2 = 10/28 = 5/14