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Question
Two dice are thrown together. Let A be the event ‘getting 6 on the first die’ and B be the event ‘getting 2 on the second die’. Are the events A and B independent?
Solution
A = {(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
B = {(1, 2), (2, 2), (3, 2), (4, 2), (5, 2), (6, 2)}
A ∩ B = {(6, 2)}
P(A) = `6/36 = 1/6`
P(B) = `1/6`
P(A ∩ B) = `1/36`
Events A and B will be independent if
P(A ∩ B) = P(A) P(B)
i.e., L.H.S = P(A ∩ B) = `1/36`
R.H.S = P(A) P(B) = `1/6 xx 1/6 = 1/36`
Hence, A and B are independent.
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