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…

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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 3^43k, then k is equal to

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Correct answer: (A) 17/8. Given n=5, p=1/4 and q=1-p=3/4 Required probability = when no machine has fault + when one machine has fault + when two machines have fault. =C0534^5+C151/434^4+C2514^234^3 =243/1024+405/1024+270/1024=918/1024=459/512=(27×17)/(64×8) ⇒34^3×k=34^3×17/8 ∴k=17/8

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

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In a workshop, there are five machines and the probability of any one of them to be out of service on a day is 14 . If the probability that at most two machines will be out of service on the same day is 343k, then k is equal to

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