SOLUTION: Suppose we flip a fair coin four times. Give the probability of observing exactly two "heads" in these four coin flips.

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Question 1167500: Suppose we flip a fair coin four times. Give the probability of observing exactly two "heads" in these four coin flips.
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!

T T T T
T T T H
T T H T
T T H H (1)
T H T T
T H T H (2)
T H H T (3)
T H H H
H T T T
H T T H (4)
H T H T (5)
H T H H
H H T T (6)
H H T H
H H H T
H H H H
P(2 heads) = 6/16 = 3/8 = 0.375

Another way: there are four chances to get two heads, and there are 2^4 possible outcomes: P(2 heads) = 4C2 / 2^4 = 6/16
And of course: 4 places to put the first H times 3 places for the 2nd H, but we divide by 2! because we've overcounted (the H's are indistinguishable) so we get (4*3/2!)/2^4 = 6/16



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