Question

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?

Answer 1

Given: A box containing 30 bulbs of which 5 are defective.Each trail is independent of the other trial.

To find: 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

P₁(success) = \(\frac{5}{30}\)

Probability of success in the second trial without replacement of the first draw is given by

P₂(success) = \(\frac{4}{29}\)

Hence , the probability that both the bulbs are chosen are defective,with each trial being independent is given by