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Question
A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Check whether A and B are independent events or not.
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Solution
The sample space of this experiment will be as follows.
S = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
A = Head appears on the coin; B = Number 3 appears on the die.
(A ∩ B) = {(H, 3}}
and n(S) = 12, n(A) = 6, n(B) = 2
and n(A ∩ B) = 1
∴ P(A) = `(n(A))/(n(S)) = 6/12 = 1/2`,
P(B) = `(n(B))/(n(S)) = 2/12 = 1/6`
and P(A ∩ B) = `(n(A ∩ B))/(n(S))`
= `1/12`
= `1/2 . 1/6`
= P(A) . P(B)
Therefore, events A and B are independent.
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