Q.

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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a

172

b

4

c

178

d

174

answer is C.

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Detailed Solution

Required probability = when no. machine has fault + when only one machine has fault + when only two machines have fault.=5C0345+5C114344+5C2142343=2431024+4051024+2701024=9181024=459512=27×1764×8=343×k=343×178∴k=178
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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: