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Mathematics

A box contains 150 bulbs out of which 15 are defective. It is not possible to just look at a bulb and tell whether or not it is defective. One bulb is taken out at random from this box. Calculate the probability that the bulb taken out is :

(i) a good one

(ii) a defective one.

Probability

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Answer

Total bulbs = 150.

No. of possible outcomes = 150

(i) Good bulbs = Total bulbs - Defective bulbs

= 150 - 15 = 135.

∴ No. of favourable outcomes = 135.

P(drawing a good bulb) = No. of favourable outcomesNo. of possible outcomes=135150=910\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{135}{150} = \dfrac{9}{10}.

Hence, probability of drawing a good bulb = 910\dfrac{9}{10}.

(ii) No. of defective bulbs = 15.

∴ No. of favourable outcomes = 15.

P(drawing a defective bulb) = No. of favourable outcomesNo. of possible outcomes=15150=110\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{15}{150} = \dfrac{1}{10}.

Hence, probability of drawing a defective bulb = 110\dfrac{1}{10}.

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