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

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?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×