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07 Dec 2019, 19:08
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B
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GMATBusters’ Quant Quiz Question -5
Ram and Shyam planned to be play a game in which they are to throw three dice each. The game-points is the sum of points on all three dice. If Ram scores 10 in his attempt what is the probability that Shaam will outscore Ram in his?
A. 24/64
B. 32/64
C. 36/64
D. 40/64
E. 42/64
Aviral1995
GMAT 1: 710 Q49 V36
Posts: 233
08 Dec 2019, 01:15
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If we see the minimum value of sum on all 3 dice its 3 and maximum value of sum on all 3 dice its 6
Since all dice has equal probability to occur. So result is directly 1/2 since probability of sum of value from 3 to 10 will be same as probability of value from 11 to 18.
Ans - B
Since all dice has equal probability to occur. So result is directly 1/2 since probability of sum of value from 3 to 10 will be same as probability of value from 11 to 18.
Ans - B
General Discussion
07 Dec 2019, 20:37
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Answer:B
Total no of outcomes=6*6*6=216
favorable outcomes >10 ae below.
Sum of 18: 6+6+6 (1 outcome meeting the criteria of sum > 10)
Sum of 17: 6+6+5 (3 outcomes: 665, 656, 566)
Sum of 16: 6+6+4 (3 outcomes), 6+5+5 (3 outcomes): total of 6 outcomes
Sum of 15: 6+6+3 (3 outcomes), 6+5+4 (6 outcomes: 654, 645, 564, 546, 465, 456), 5+5+5 (1 outcome): total of 10 outcomes
Sum of 14: 6+6+2 (3), 6+5+3 (6), 6+4+4 (3), 5+5+4 (3): total of 15 outcomes
Sum of 13: 6+6+1 (3), 6+5+2 (6), 6+4+3 (6), 5+5+3 (3), 5+4+4 (3): total of 21 outcomes
Sum of 12: 6+5+1 (6), 6+4+2 (6), 6+3+3 (3), 5+5+2 (3), 5+4+3 (6), 4+4+4 (1): total of 25 outcomes
Sum of 11: 6+4+1 (6), 6+3+2 (6), 5+5+1 (3), 5+4+2 (6), 5+3+3 (3), 4+4+3 (3): total of 27 outcomes
Outcomes >10 = 108
108/216=1/2
@ bunnel you should help me if there is a short cut for this pls.
Total no of outcomes=6*6*6=216
favorable outcomes >10 ae below.
Sum of 18: 6+6+6 (1 outcome meeting the criteria of sum > 10)
Sum of 17: 6+6+5 (3 outcomes: 665, 656, 566)
Sum of 16: 6+6+4 (3 outcomes), 6+5+5 (3 outcomes): total of 6 outcomes
Sum of 15: 6+6+3 (3 outcomes), 6+5+4 (6 outcomes: 654, 645, 564, 546, 465, 456), 5+5+5 (1 outcome): total of 10 outcomes
Sum of 14: 6+6+2 (3), 6+5+3 (6), 6+4+4 (3), 5+5+4 (3): total of 15 outcomes
Sum of 13: 6+6+1 (3), 6+5+2 (6), 6+4+3 (6), 5+5+3 (3), 5+4+4 (3): total of 21 outcomes
Sum of 12: 6+5+1 (6), 6+4+2 (6), 6+3+3 (3), 5+5+2 (3), 5+4+3 (6), 4+4+4 (1): total of 25 outcomes
Sum of 11: 6+4+1 (6), 6+3+2 (6), 5+5+1 (3), 5+4+2 (6), 5+3+3 (3), 4+4+3 (3): total of 27 outcomes
Outcomes >10 = 108
108/216=1/2
@ bunnel you should help me if there is a short cut for this pls.
