maths disvisible problems

2014-04-28 5:51 am
Mary and Peter are playing a game:

Each of them is rolling a die. If the sum of the two dice is divisible by 4,Mary will pay Peter 10 dollars. How much should Peter pay Mary when the total is notdivisible by 4 in order to make the game fair?

(A fair game is a game in whichthe expected winnings for each of them is 0 dollar.)

回答 (1)

2014-04-28 11:08 am
✔ 最佳答案
No.of combinations without restriction
= 6²
= 36

Combinations that the sum is divisible by 4 :
A sum of 4 : (1,3), (2,2), (3,1)
A sum of 8 : (2,6), (3,5), (4,4), (5,3), (6,2)
A sum of 12 : (6, 6)

P(divisible by 4) = (9/36) = 1/4
P(not divisible by 4) = 1 - (1/4) = 3/4

Let n dollars be the amount that Peter should pay Mary when the total is notdivisible by 4.

10 x (1/4) = n x (3/4)
n = 10/3

Hence, Peter should pay Mary
= 10/3 dollars.
= 3.33 dolloars (to 2 decimalplaces)
參考: 土扁


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