# It is observed that it rains on 12 days out of 30 days. Find the probability that it rains exactly 3 days of week. - Mathematics and Statistics

Sum

It is observed that it rains on 12 days out of 30 days. Find the probability that it rains exactly 3 days of week.

#### Solution

Let X = number of days it rains in a week.

p = probability that it rains

∴ p = 12/30 = 2/5

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

Given: n = 7

∴ X ~ B (7, 2/5)

The p.m.f. of X is given by

P(X = x) = "^nC_x  p^x  q^(n - x)

i.e. p(x) = "^7C_x  (2/5)^x  (3/5)^(7 - x) x = 0, 1, 2, ...., 7

P(it rains exactly 3 days of week) = P(X = 3)

= p(3) = "^7C_3  (2/5)^3  (3/5)^(7 - 3)

= (7 xx 6 xx 5)/(3 xx 2 xx 1) (8/125)(81/625)

= 35(8/125)(81/625) = (35 xx 8 xx 81)/5^7

= 22680/78125 = 0.2903

Hence, the probability that it rains exactly 3 days of week = 35 xx 8 xx 81/5^7 OR 0.2903.

Concept: Binomial Distribution
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 8 Binomial Distribution
Miscellaneous exercise 8 | Q 15.1 | Page 255