SOLUTION: What is the probability that three number cubes rolled at the same time will show three different numbers?
Algebra ->
Probability-and-statistics
-> SOLUTION: What is the probability that three number cubes rolled at the same time will show three different numbers?
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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.
