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Question
What are the chances that the first roll on a die was a four if it was rolled three times and the sum of the numbers appearing on the upper face is 15?
What are the chances that the first roll on a die was a four if it was rolled three times and the sum of the numbers appearing on the upper face is 15?
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Solution
The correct option is D
The sum of numbers can be 15 in the following three ways:
Case I: 15=3+6+6
Total number of ways in which 3,6 and 6 can be obtained = 3
Case II: 15=4+5+6
Total number of ways in which 4,5 and 6 can be obtained = 6
Case III: 15=5+5+5
Total number of ways in which 5,5, and 5 can be obtained = 1
Hence, the total number of ways = 3+6+1 = 10
The total number of ways in which the first roll will be 4 is 2 i.e. (4,5,6) or (4,6,5).
∴ Required probability = 210 = 15
The sum of numbers can be 15 in the following three ways:
Case I: 15=3+6+6
Total number of ways in which 3,6 and 6 can be obtained = 3
Case II: 15=4+5+6
Total number of ways in which 4,5 and 6 can be obtained = 6
Case III: 15=5+5+5
Total number of ways in which 5,5, and 5 can be obtained = 1
Hence, the total number of ways = 3+6+1 = 10
The total number of ways in which the first roll will be 4 is 2 i.e. (4,5,6) or (4,6,5).
∴ Required probability = 210 = 15
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