Night reader wrote:When a certain coin is flipped, the probability of heads is 0.5. If the coin is flipped 6 times, what is the probability that there are exactly 3 heads?
A. 1/4
B. 1/3
C. 5/16
D. 31/64
E. 1/2
[spoiler]only mental math and calc took me around 75 sec; one needs time to mind cases, selections and other blas ...[/spoiler]
Step 1: Determine the probability of one way to get a good outcome
P(HHHTTT) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/64
Step 2: Count all the possible ways to get a good outcome
Number of ways to arrange HHHTTT = 6!/(3!3!) = 20
or
Number of ways to get a combination of 3 heads from 6 choices = 6C3 = 20
Step 3: Multiply the results of Steps 1 and 2
1/64 * 20 = 5/16.
The correct answer is
C.
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