ruplun wrote:probability of raining on any day in a week is 50 % .what is the prob that it rains exactly 3 days in a span of 5 days?
P(exactly n times) = P(one way) * total possible ways.
Let R = rain and N = no rain.
P(one way):
One way to get exactly 3 days of rain is to have rain on the first 3 days but not on the last 2 days.
P(RRRNN) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32.
Total possible ways:
Any arrangement of the letters RRRNN will yield exactly 3 days of rain.
Thus, to account for all the ways to get exactly 3 days of rain, the result above needs to be multiplied by the number of ways to arrange RRRNN.
Number of ways to arrange RRRNN = 5!/(3!2!) = 10.
Multiplying the results above, we get:
P(exactly 3 days of R) = 10 * 1/32 = 10/32 = 5/16.
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