標題:
maths disvisible problems
發問:
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... 顯示更多 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.)
最佳解答:
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)
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