The probability of rain on any given day in a region is found to be 0.1 based on

melodykap

melodykap

Answered question

2021-09-30

The probability of rain on any given day in a region is found to be 0.1 based on the Binomial probability distribution.
a) What is the probability of 4 days with rain in one week?
b) What is the probability that it will rain in the next 4 days?
c) What is the probability that it will rain 4 consecutive days after 3 days with no rain in one week?

Answer & Explanation

yunitsiL

yunitsiL

Skilled2021-10-01Added 108 answers

Step 1
Probability of rain on any given day, p=0.1
Probability of not raining on any given day , 1p=10.1=0.9
Given Binomial probability distribution
P(X)=n!X!(nX)!pX(1p)nX
Step 2
a) Probability Event =Pr(X=4)
This implies that
Pr(X=4)=(74)0.14×0.974
=0.0026
the probability of 4 days with rain in one week is Pr(X=4)=0.0026
b) Probability of rain on any given day, p=0.1
Then,
Probability of rain in next 4 days =0.10.10.10.1=0.0001
c) Probability of no rain in 3 days =0.90.90.9=0.729
Probability of rain in 4 consecutive days =0.10.10.10.1=0.0001
and There are fours ways to arrange the event in a given week
Required Probability =40.00010.729=0.000291

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