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

Answer 1

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`