Question

In a workshop, there are five machines and the probability of any one of them to be out of service on a day is `1/4`. If the probability that at most two machines will be out of service on the same day is `(3/4)^3k`, then k is equal to ______.

विकल्प

• `17/8`

• `18/8`

• `19/8`

• `20/8`

Answer 1

In a workshop, there are five machines and the probability of any one of them to be out of service on a day is `1/4`. If the probability that at most two machines will be out of service on the same day is `(3/4)^3k`, then k is equal to `underlinebb(17/8)`.

Explanation:

Required probability = when no machine has fault + when only one machine has fault + when only two machines have fault.

= `""^5C_0(3/4)^5 + ""^5C_1(1/4)(3/4)^4 + ""^5C_2(1/4)^2(3/4)^3`

= `243/1024 + 405/1024 + 270/1024`

= `918/1024`

= `(27 xx 17)/(64 xx 8)`

= `459/512`

⇒ `(3/4)^3 xx k = (3/4)^3 xx 17/8`

∴ k = `17/8`