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In a lot of 500 wristwatches, 50 are found to be defective. One watch is drawn uniformly at random from the box. Find the Probability that the chosen wristwatch is defective.

Last updated date: 14th Jul 2024
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Hint: Probability of event E = $\dfrac{n(E)}{n(S)}=\dfrac{\text{Favourable cases}}{\text{Total number of cases}}$ where S is called the sample space of the random experiment. Find n (E) and n (S) and use the above formula to find the Probability.

Complete step-by-step answer:

Let E be the event: The watch chosen is defective.
Since there are 50 defective watches the total number of cases favourable to E = 50.
Hence, we have n(E) = 50.
The total number of ways in which we can choose the wrist watches = 500.
Hence, we have n(S) = 500.
Hence, P (E) = $\dfrac{50}{500}=0.1$
Hence the Probability that the chosen wristwatch is defective = 0.1
[1] It is important to note that drawing uniformly at random is important for the application of the above problem. If the draw is not random, then there is a bias factor in drawing, and the above formula is not applicable. In those cases, we use the conditional probability of an event.
[2] The Probability of an event always lies between 0 and 1
[3] The sum of Probabilities of an event E and its complement E’ is 1.
i.e. $P(E)+P(E')=1$
Hence, we have $P(E')=1-P(E)$. This formula is applied when it is easier to calculate P(E’) instead of P(E).