fangtray wrote:A coin is tossed five times. What is the probability of obtaining exactly two heads in the five tosses?
thanks.
P(exactly n times) = P(one way) * total possible ways.
P(one way):
One way to get exactly 2 heads is to get heads on the first 2 flips and tails on the last 3 flips.
P(HHTTT) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32.
Total possible ways:
Any arrangement of the letters HHTTT will yield exactly 2 heads.
Thus, to account for all the ways to get exactly 2 heads, the result above needs to be multiplied by the number of ways to arrange HHTTT.
Number of ways to arrange HHTTT = 5!/(2!3!) = 10.
Multiplying the results above, we get:
P(exactly 2 heads) = 10 * 1/32 = 10/32 = 5/16.
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