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Question

A lot of 20 bulbs contain 4 defective ones. One bulb is selected at random from the lot. What is the probability that this bulb is defective?

Suppose the bulb selected in the previous case is not defective and is not replaced. Now one bulb is selected at random from the rest. What is the probability that this bulb is not defective?


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Solution

Step 1: Find the probability that the selected bulb is defective.

We have,

Total number of bulbs =20

Number of defective bulbs =4

Probability of getting defective bulbs =numberofdefectivebulbstotalnumberofbulbs

=420

=15

Hence, probability that the selected bulb is defective is 15.

Step 2: Find the probability that the selected bulb is not defective.

Since, 1 non-defective bulb is drawn and is not replaced, then the total number of bulbs left are (20-1)=19.

And, the number of non-defective bulbs =194=15

Probability of getting non-defective bulbs =numberofnon-defectivebulbstotalnumberofbulbs

=1519

Hence, the probability that the selected bulb is not defective is 1519


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