CUET · MATHS · PYQ PAPER 2023
Number of defective bulbs in a lot of 500 bulbs follows a binomial distribution with probability of a randomly selected bulb to be defective equal to 0.3.
A sample of 50 bulbs is drawn. Probability of 2 defective bulbs in the sample is:
- A \(1225(0.7)^{50}\)
- B \(2450(0.3)^2(0.7)^{48}\)
- C \(1225(0.3)^2(0.7)^{48}\)
- D \(1225(0.3)^{50}\)
Answer & Solution
Correct Answer
(C) \(1225(0.3)^2(0.7)^{48}\)
Step-by-step Solution
Detailed explanation
\( P(X=k) = \binom{n}{k} p^k (1-p)^{n-k} \) \( \binom{50}{2} = \frac{50 \times 49}{2 \times 1} = 1225 \) \( P(X=2) = 1225 (0.3)^2 (1-0.3)^{50-2} \) \( P(X=2) = 1225 (0.3)^2 (0.7)^{48} \)
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