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 $\mathbf{1}$: 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 $=\frac{numberofdefectivebulbs}{totalnumberofbulbs}$ $=\frac{4}{20}$ $=\frac{1}{5}$Hence, probability that the selected bulb is defective is $\frac{\mathbf{1}}{\mathbf{5}}$.Step $\mathbf{2}$: 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 $\left(20-1\right)=19$.And, the number of non-defective bulbs $=19–4=15$Probability of getting non-defective bulbs $=\frac{numberofnon-defectivebulbs}{totalnumberofbulbs}$ $=\frac{15}{19}$Hence, the probability that the selected bulb is not defective is $\frac{\mathbf{15}}{\mathbf{19}}$

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