Question

A bag contains 6 black and 8 white balls. One ball is drawn uniformly at random. What is the probability that the ball drawn is white?
[a] $\dfrac{3}{4}$
[b] $\dfrac{4}{7}$
[c] $\dfrac{1}{8}$
[d] $\dfrac{3}{7}$

Answer 1

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 ball drawn is white.
Since there are 8 white balls the total number of cases favourable to E = 8.
Hence, we have n (E) = 8.
The total number of ways in which we can draw a ball out of the bag = 8+6 = 14.
Hence, we have n (S) = 14.
Hence, P (E) = $\dfrac{8}{14}=\dfrac{4}{7}$.
Hence the probability that the chosen wristwatch is defective $=\dfrac{4}{7}$.
Hence option [b] is correct.

Note: [1] It is important to note that drawing balls 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’ = 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).