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Home » There is a box containing 30 bulbs, of which 5 are defective. If two bulbs are chosen at random from the box in succession without replacing the first, what is the probability that both the bulbs are chosen are defective?
There is a box containing 30 bulbs, of which 5 are defective. If two bulbs are chosen at random from the box in succession without replacing the first, what is the probability that both the bulbs are chosen are defective?
CBSE | Class 12 | Exercise 29B | Maths | Probability | RS Aggarwal
There is a box containing 30 bulbs, of which 5 are defective. If two bulbs are chosen at random from the box in succession without replacing the first, what is the probability that both the bulbs are chosen are defective?

Let, success :bulb chosen is defective .i.e \frac{5}{30}
Now, the Probability of success in the first trial is
P_{1}(\text { success })=\frac{5}{30}
Probability of success in the second trial without replacement of the first draw is given by
\mathrm{P}_{2}(\text { success })=\frac{4}{29}
Hence, the probability that both the bulbs are chosen are defective, with each trial being independent is given by
\mathrm{P}_{1} \times \mathrm{P}_{2}=\frac{5}{30} \times \frac{4}{29}=\frac{2}{87}

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