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प्रश्न
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
उत्तर
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`.
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