JEE Mains · Maths · STD 12 - 13. probability
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 \(\left(\frac{3}{4}\right)^{3} \mathrm{k},\) then \(\mathrm{k}\) is equal to
- A \(\frac{17}{2}\)
- B \(4\)
- C \(\frac{17}{8}\)
- D \(\frac{17}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{17}{8}\)
Step-by-step Solution
Detailed explanation
Probability that at most \(2\) machines are out of service \(=\mathrm{^{5}C}_{0}\left(\frac{3}{4}\right)^{5}+^{5} \mathrm{C}_{1}\left(\frac{3}{4}\right)^{4}\left(\frac{1}{4}\right)+^{5} \mathrm{C}_{2}\left(\frac{3}{4}\right)^{3}\left(\frac{1}{4}\right)^{2}\)…
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