CUET · MATHS · PYQ PAPER 2025
There are 50 telephone lines in an exchange. The probability that any one of them will be busy is 0.1, then the probability that all the lines are busy?
- A \(\frac{e^{-5} \times 5^{50}}{5!}\)
- B \(\frac{e^{-5} \times 5^{50}}{50!}\)
- C \(\frac{e^{-50} \times 50^{50}}{50!}\)
- D \(\frac{e^{-50} \times 50^5}{50!}\)
Answer & Solution
Correct Answer
(B) \(\frac{e^{-5} \times 5^{50}}{50!}\)
Step-by-step Solution
Detailed explanation
\( n = 50 \) \( p = 0.1 \) \( \lambda = n p = 50 \times 0.1 = 5 \) \( P(X=50) = \frac{e^{-\lambda} \lambda^{50}}{50!} = \frac{e^{-5} 5^{50}}{50!} \)
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