Maharashtra State BoardHSC Arts 12th Board Exam
Advertisement Remove all ads

It is observed that it rains on 12 days out of 30 days. Find the probability that it it will rain at least 2 days of given week. - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Sum

It is observed that it rains on 12 days out of 30 days. Find the probability that it it will rain at least 2 days of given week.

Advertisement Remove all ads

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 will rain on at least 2 days of given week)

= P(X ≥ 2) = 1 - P(X < 2)

= 1 - [P(X = 0) + P(X = 1)]

`= 1 - [""^7C_0  (2/5)^0  (3/5)^(7 - 0) + "^7C_1  (2/5)^1  (3/5)^(7 - 1)]`

`= 1 - [1(1)(3/7)^7 + 7(2/5)(3/5)^6]`

`= 1 - [3/5 + 14/5](3/5)^6`

`= 1 - (17/5)(729/(5)^6) = 1 - 12393/5^7`

`= 1 - 12393/78125 = 1 - 0.1586`

= 0.8414

Hence, the probability that it rains at least 2 days of given week = `1 - 12393/5^7` OR 0.8414

Concept: Binomial Distribution
  Is there an error in this question or solution?

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 8 Binomial Distribution
Miscellaneous exercise 8 | Q 15.2 | Page 255
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×