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