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

A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of at least 5 successes. - Mathematics and Statistics

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

A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of at least 5 successes.

Advertisement Remove all ads

Solution

Let X = number of successes, i.e. number of odd numbers.

p = probability of getting an odd number in a single throw of a die

∴ p = `3/6 = 1/2` and q = `1 - "p" = 1 - 1/2 = 1/2`

Given: n = 6

∴ X ∼ B`(6, 1/2)`

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

`p("X = x") = "^nC_x  p^x  q^(n - x)`

i.e. p(x) = `"^6C_x (1/2)^x (1/2)^(6 - x)`

` = "^6C_x (1/2)^6,` x = 0, 1, 2, ...,6

P(at least 5 successes) = P[X ≥ 5]

= p(5) + p(6)

`= ""^6C_5 (1/2)^6 + "^6C_6 (1/2)^6`

`= (""^6C_5 + "^6C_6) (1/2)^6`

`= (6 + 1) 1/64 = 7/64`

Hence, the probability of at least 5 successes is `7/64`.

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

APPEARS IN

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×