Maths Problem(dice probability)
2006-12-11 3:28 pm
Two six-sided dice are fair in that each face has the same probability of turing up. One of the dice had been changed so that the four was replaced with a three. The other had the three replaced with a four. When these dice are thrown, what is the probability that the sum is an odd number?
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2006-12-12 1:49 am
✔ 最佳答案
This is a Maths problem, should get the answer by calculation!======
1st dice : 1,2,3,3,5,6
Chance for ODD number = 4/6 = 2/3
Chance for EVEN number = 2/6 = 1/3
2nd dice : 1,2,4,4,5,6
Chance for ODD number = 2/6 = 1/3
Chance for EVEN number = 4/6 = 2/3
If the sum of the 2 dices is an odd number, that is either of the following cases:
- 1st dice is ODD + 2nd dice is EVEN = 2/3 * 2/3 = 4/9
- 1st dice is EVEN + 2nd dice is ODD = 1/3 * 1/3 = 1/9
Therefore, the probability that the sum is an odd number is 4/9 + 1/9 = 5/9
2006-12-11 6:50 pm
Assume the possible outcome for the first dice be = {1, 2, 3, 3, 5, 6}
and the possible outcome for the second dice be = {1, 2, 4, 4, 5, 6}
Total number of possible outcomes = 6 x 6 = 36
The possible cases for the sum of 2 dices be an odd number are:
Case 1
1st dice = 1, 2nd dice = 2, sum = 3
Cases 2 and 3
1st dice = 1, 2nd dice = 4, sum = 5
Case 4
1st dice = 1, 2nd dice = 6, sum = 7
Case 5
1st dice = 2, 2nd dice = 1, sum = 3
Case 6
1st dice = 2, 2nd dice = 5, sum = 7
Cases 7 and 8
1st dice = 3, 2nd dice = 2, sum = 5
Cases 9, 10, 11 and 12
1st dice = 3, 2nd dice = 4, sum = 7
Cases 13 and 14
1st dice = 3, 2nd dice = 6, sum = 9
Case 15
1st dice = 5, 2nd dice = 2, sum = 7
Cases 16 and 17
1st dice = 5, 2nd dice = 4, sum = 9
Case 18
1st dice = 5, 2nd dice = 6, sum = 11
Case 19
1st dice = 6, 2nd dice = 1, sum = 7
Case 20
1st dice = 6, 2nd dice = 5, sum = 11
Probability (Sum of 2 dice = Odd Number)
= 20/ 36
= 5/9
and the possible outcome for the second dice be = {1, 2, 4, 4, 5, 6}
Total number of possible outcomes = 6 x 6 = 36
The possible cases for the sum of 2 dices be an odd number are:
Case 1
1st dice = 1, 2nd dice = 2, sum = 3
Cases 2 and 3
1st dice = 1, 2nd dice = 4, sum = 5
Case 4
1st dice = 1, 2nd dice = 6, sum = 7
Case 5
1st dice = 2, 2nd dice = 1, sum = 3
Case 6
1st dice = 2, 2nd dice = 5, sum = 7
Cases 7 and 8
1st dice = 3, 2nd dice = 2, sum = 5
Cases 9, 10, 11 and 12
1st dice = 3, 2nd dice = 4, sum = 7
Cases 13 and 14
1st dice = 3, 2nd dice = 6, sum = 9
Case 15
1st dice = 5, 2nd dice = 2, sum = 7
Cases 16 and 17
1st dice = 5, 2nd dice = 4, sum = 9
Case 18
1st dice = 5, 2nd dice = 6, sum = 11
Case 19
1st dice = 6, 2nd dice = 1, sum = 7
Case 20
1st dice = 6, 2nd dice = 5, sum = 11
Probability (Sum of 2 dice = Odd Number)
= 20/ 36
= 5/9
參考: myself
收錄日期: 2021-04-12 22:49:58
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