Question

He probability of rain on any given day is 2/3. What is the probability of at most one day of rain during the next 3 days?

Answer 1

Probability of at most one day of rain during next three day is `7/27` or about `26%`

Explanation:

At most one day of rain during next three days means rain on not more than one day during next three days.

Let `R` denote rain on the day and `N` denote no rain on the day. Further let `XXX` denote `R` or `N` on next three days.

Ten we are looking for a pattern i.e. `RN N`,`NRN`, `N NR` or `N N N`.

Now as the probability of rain i.e. `R` is `2/3`, probability of `N` is `1/3`

and hence `P(RN N)=P(NRN)=P(N NR)=2/3xx1/3xx1/3=2/27`

and P(N N N)=1/3xx1/3xx1/3=1/27#

Hence, the probability of at most one day of rain during next three day is `3xx2/27+1/27=7/27` or about `26%`