Probability question about tossing coins
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Probability question about tossing coins

[From: ] [author: ] [Date: 13-07-04] [Hit: ]
we conclude that B independent of A.Now P(A l B) = P(A n B) / P(B) = (3/16) / (3/8) = 1/2 = P(A),conclude that A is independent of B.Thus A and B are independent events.......
This is the question, and i dont really know where to start.. --> Suppose that a fair coin is tossed four times. 'A' is the event that the first toss yields heads and 'B' is the event that 2 heads and 2 tails occur. Are 'A' and 'B' independent events? Explain.

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Recall that P(B l A) = P(B n A) / P(A).

Now P(A) = 1/2. There are 2^4 = 16 possible outcomes from the four tosses.
8 of these outcomes have a head as the first toss, and 3 of these 8 outcomes
are such that there are a total of 2 heads and 2 tails after 4 tosses.
Thus P(B n A) = 3/16, and so P(B l A) = (3/16) / (1/2) = 3/8.

Next, P(B) = [4!/(2!*2!)] / 16 = 6/16 = 3/8. Since P(B l A) = P(B)
we conclude that B independent of A.

Now P(A l B) = P(A n B) / P(B) = (3/16) / (3/8) = 1/2 = P(A), so we can
conclude that A is independent of B.

Thus A and B are independent events.
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