If the occurrence of a rainy day has probability of 0.25 and
is statistically independent of it...

Question

If the occurrence of a rainy day has probability of 0.25 and
is statistically independent of it raining in the previous and in the following
days, calculate (a) the probability of 4 rainy days in a week; (b) the
probability that the next 4 days will be rainy; and (c) the probability of 4
rainy days in a row and 3 dry days in a week

Monica · Accepted Answer

Solution 
Given:
The probability of a rainy day is 0.25 
a) The probability of four rainy days is given by,
Total number of  days in a week is 7
Total number of rainy days is 4 
Probability of 4 rainy day is 0.25
Using binomial function in excel 
=1-Binom.dist(7,3,0.75,1)
=1 – 0.070557
=0.

If the occurrence of a rainy day has probability of 0.25 and is statistically independent of it raining in the previous and in the following days, calculate (a) the probability of 4 rainy days in a...

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