Question

Five good light bulbs and two defective ones were mixed up unknowingly. To identify the defective ones for disposal, the bulbs are tested one one by one. If both defective ones are identified in the testing of the second one, what is the probability of this event?

Answer 1

The probability of the event of identifying both the defective bulb in the second attempt is
`(1)/(21)`.

Explanation:

The number of good light bulbs is 5 and the number of defective bulbs is 2.

It is provided that when a defective bulb is found in the inspection it is disposed.

If a defective bulb is found in the first trial the probability of his event is
`(2)/(7)`.

Now the remaining number of bulbs is 6.

If a defective bulb is found in the second trial the probability of his event is
`(1)/(6)`.

So the probability of identifying both the defective bulb in the second attempt is:

P (Selecting a defective bulb in 1st attempt) × P (Selecting a defective bulb in 2nd attempt) =

`=(2)/(7)*(1)/(6) \\=(1)/(21)`

Thus, the probability of the event of identifying both the defective bulb in the second attempt is
`(1)/(21)`.