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 more than 8 bulbs work properly

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")`

More than 8 bulbs work properly

We can say that less than 2 bulbs are defective

P(x < 2) = P(x = 0) + P(x = 1)

= `""^10"C"_0 (1/50)^0 (49/50)^10 + ""^10"C"_1 (1/50)^1 (49/50)^9`

= `(49/50)^10 + 1/5(49/50)^9`

= `(49/50)^9 (49/50 + 1/5)`

= `(49/50)^9 (59/50)`

= `(59(49^9))/(50)^10`.