Question

Your friend rolls a standard six-sided die 1200 times and you write down the number of times each outcome comes up (the number of 1’s, the number of 2’s, the number of 3’s, etc.). Note that the probability that any single outcome comes up when the die is rolled is 1/6.

Suppose you and your friend make a bet before the 1200 rolls take place. You agree that you will pay your friend $1 for every roll that comes up a 3 or a 4, and your friend will pay you $3 for every roll that comes up a 5. No money will be exchanged for rolls that come up 1, 2, or 6.

Who do you expect will make more money on this deal? How much more money will that person make?

A) You---$200 more than your friend.

B) Your friend---$200 more than you.

C) You---$600 more than your friend.

Answer 1

A) You---$200 more than your friend.

Explanation:

Theoretically, each number on the dice has an equal chance of being rolled. Therefore, you take the total number of rolls 1200 and divide by the amount of numbers on the dice 6, and you get 200, that means each number will get rolled 200 times. For a 3 or a 4 rolled which totals up 400 times your friend gets payed $1 by you, your friend gets $400. For a 5 which is only rolled 200 times your friend will have to pay you $3, which will total to $600 you get paid. Finally, take the difference in $400 and $600 and it is $200, in the end you end up with $200 more than your friend.