Question & Answer
QUESTION

A bag contains 6 black and 8 white balls. One ball is drawn 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 Verified Verified
Hint: For solving this problem, first calculate the sample space of drawing a ball from the bag containing a total 14 balls. The favourable outcome is the event of drawing a white ball. Now we can easily calculate the required probability.

Complete Step-by-Step solution:
In mathematics, the possibility of occurrence of an event falls under the category of probability. As given in the problem statement, a white ball is drawn. If a random experiment is performed, then each of its outcomes is known as an elementary event. The set of all possible outcomes of a random experiment is called the sample space associated with it and it is generally denoted by ‘S’.
The total number of white balls $=8$.
The total number of black balls$=6$.
The total number of balls in the bag is equal to the sum of the total number of white balls and black balls\[=8+6=14\].
We use the formula of occurrence of an Event $=\dfrac{\text{Number of Favourable Outcomes}}{\text{Total Number of Possible Outcomes}}$
Probability of getting a white ball $=\dfrac{\text{Total number of white ball}}{\text{Total number of balls}}$
Probability of getting a white ball from the bag $=\dfrac{8}{14}=\dfrac{4}{7}$.
Hence, the probability of getting a white ball is $\dfrac{4}{7}$.
Therefore, option (b) is correct.

Note: The key concept for solving a problem is the knowledge of probability of occurrence of an event. Students must be careful while calculating the space for favourable events. There should be no redundancy of particular events in the favourable outcomes.