He probability of rain on any given day is \frac{2}{3}.

Kiribatiyo2

Kiribatiyo2

Answered question

2022-02-11

He probability of rain on any given day is 23. What is the probability of at most one day of rain during the next 3 days?

Answer & Explanation

illustrationsamk

illustrationsamk

Beginner2022-02-12Added 14 answers

Step 1
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 RNN, NRN, NNR or NNN
Now as the probability of rain i.e. R is 23, probability of N is 13
and hence P(RNN)=P(NRN)=P(NNR)
=23×13×13=227
and
P(NNN)=13×13×13=127
Hence, the probability of at most one day of rain during next three day is
3×227+127=727
or about 26%

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