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Question
A factory produces bulbs. The probability that anyone bulb is defective is `1/50` and they are packed in boxes of 10. From a single box, find the probability that exactly two bulbs are defective
Solution
Let X be the random variable denoting a bulb to be defective.
Here, n = 10
p = `1/50`
q = `1 - 1/50 = 49/50`
We know that P(X = r) = `""^"n""C"_"r" "p"^"r" "q"^("n" - "r")`
Exactly two bulbs are defective
∴ P(x = 2) = `""^10"C"_2 (1/50)^2 (49/50)^(10 - 2)`
= `45 * (49)^8/(50)^10`
= `45 xx (1/50)^10 xx (49)^8`
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