SOLUTION: What is the probability that three number cubes rolled at the same time will show three different numbers?
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Question 1180752: What is the probability that three number cubes rolled at the same time will show three different numbers?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
Even though the problem says the three dice are rolled at the same time, you can think of them as being rolled one at a time. Then find the answer to the question by finding the probability that each successive roll gives you the desired outcome.
The first roll can be any of the 6 numbers:
P(okay after 1st roll) = 6/6 = 1.
The second roll must be one of the 5 remaining numbers:
P(second roll okay) = 5/6; P(okay after second roll) = (1)(5/6) = 5/6.
The third roll must be one of the 4 remaining numbers:
P(third roll okay) = 4/6; P(okay after third roll) = (5/6)(4/6) = 20/36 = 5/9.
ANSWER: 5/9
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