A fair die is rolled six times. If on the ith roll, 1 ≤ x ≤ 6, the outcome is i, we say that...
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A fair die is rolled six times. If on the ith roll, 1 ≤ x ≤ 6, the outcome is i, we say that...

[From: ] [author: ] [Date: 12-02-14] [Hit: ]
we say that a match has occurred. What is the probability that at least one match occurs?-Each roll is independent.The probability of no match on the first roll is 5/6 = .The probabilty of no match on any roll is .833333^6 = 0.......
A fair die is rolled six times. If on the ith roll, 1 ≤ x ≤ 6, the outcome is i, we say that a match has occurred. What is the probability that at least one match occurs?

-
Each roll is independent.
The probability of no match on the first roll is 5/6 = .833333
The probabilty of no match on any roll is .833333^6 = 0.334897977

The probability of at least one match is 0.665102023

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Prob(match = 0) = 6/6 * 5/6 * 4/6 * 3/6 * 2/6 * 1/6 = 0.0154

P(match >= 1) = 1 - Prob(match = 0) = 1 - 0.0154 = 0.9846
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