Question

A city of Punjab has a 15 percent chance of wet weather on any given day. What is the probability that it will take a week for it three wet weather on 3 separate days?

Answer 1

Answer: 0.0617

Step-by-step explanation:

Given: The probability of wet weather on any given day in a city of Punjab : p=15%=0.15

Let X be a binomial variable that represents the number of days having wet weather.

Binomial probability formula :
`P(X=x)=^nC_xp^x(1-p)^x`, where n= total outcomes, p = probability of success in each outcomes.

Here, n= 7 ( 1 week = 7 days)

The probability that it will take a week for it three wet weather on 3 separate days:

`P(X=3)^=\ ^7C_3(0.15)^3(1-0.15)^(7-3)\\\\=(7!)/(3!(7-3)!)(0.15)^3(0.85)^4\\\\=(7*6*5)/(3*2)* 0.003375*0.52200625\approx0.0617`

Hence, the required probability =0.0617