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A black die, a red die and a green die are thrown at the same time. What is the probability that the sum of three numbers that turn up is 15?
  • a)
    11/216
  • b)
    5/108
  • c)
    9/216
  • d)
    12 x 1/18
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A black die, a red die and a green die are thrown at the same time. Wh...
Total number o f outcom es when three dice are thrown = 6 x 6 x 6 = 216
For sum of numbers to be 15, possible ways are, (6, 6, 3), (6, 3, 6), (3, 6, 6), (6, 5, 4), (6, 4, 5), (5, 4, 6), (5, 6, 4), (4, 5, 6), (4, 6, 5), (5, 5, 5)
∴ Number of favorable outcomes = 10
∴ Required probability = 10/216 = 5/108
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Community Answer
A black die, a red die and a green die are thrown at the same time. Wh...
Calculation

The total number of outcomes when throwing three dice simultaneously is 6 x 6 x 6 = 216.

Favorable outcomes

To find the number of favorable outcomes where the sum of three numbers is 15, we can list all the possible combinations:
- (3, 6, 6)
- (4, 5, 6)
- (4, 6, 5)
- (5, 4, 6)
- (5, 6, 4)
- (6, 3, 6)
- (6, 4, 5)
- (6, 5, 4)
- (6, 6, 3)

There are a total of 9 favorable outcomes.

Probability calculation

Probability = Number of favorable outcomes / Total number of outcomes
Probability = 9 / 216
Probability = 1 / 24
Probability = 5 / 108

Therefore, the probability that the sum of three numbers that turn up is 15 is 5/108. So, option (b) is correct.
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