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Two fair dice are thrown. What is the probability that the score on the first die is 6 or the score on the second die is 5?
I think these two events are not mutually exclusive.
Let S = 6
Let F = 5
P(S or F) = P(S or F) = P(S) + P(F) − P(S and F)
There is one 6 and one 5 per die.
P(S) = 1/6
P(F) = 1/6
P(S) + P(F) = 1/6 + 1/6
P(S and F) = 1/6 • 1/6
P(S or F) = 1/6 + 1/6 - 1/36
P(S or F) = 2/6 - 1/36
LCD = 36
P(S or F) = 12/36 - 1/36
P(S or F) = 11/36
I think these two events are not mutually exclusive.
Let S = 6
Let F = 5
P(S or F) = P(S or F) = P(S) + P(F) − P(S and F)
There is one 6 and one 5 per die.
P(S) = 1/6
P(F) = 1/6
P(S) + P(F) = 1/6 + 1/6
P(S and F) = 1/6 • 1/6
P(S or F) = 1/6 + 1/6 - 1/36
P(S or F) = 2/6 - 1/36
LCD = 36
P(S or F) = 12/36 - 1/36
P(S or F) = 11/36