Question

On an average rain falls on 12 days in every 30 days find probability that on 3 days of given week

Answer 1

number of favourable observation by total number of observation is the formula

Answer 2

Answer:

0.847694

Step-by-step explanation:

Probability that rain falls on a day = p = 12/30 = 2/5

q = 1 - p = 1 - 2/5 = 3/5

n = 7

According to Binomial distribution, P(r)=nCr*q^n-r*p^r

Required probability is P(r=/>3) = 1- P(r=/<2)

Probability that rain will fall on at least 3 days of a given week = 1 - (7C0*(3/5)^7*(2/5)^0 + 7C1*(3/5)^6*(2/5)^1 + 7C2*(3/5)^5*(2/5)^2)

= 1 - (1*2187/78125*1 + 7*729/15625*2/5 + 21*243/3125*4/25)

= 1 - (2187/78125 + 729/15625 + 243/3125)

= 1 - (0.02799+0.046656+0.07766)

= 1-0.152306 = 0.847694