Question

A bag contains 4 red balls, 6 blue balls and 3 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is not blue?
A. $\dfrac{6}{13}$
B. $\dfrac{3}{13}$
C. $\dfrac{7}{13}$
D. None

Answer 1

Hint: We will use the formula for finding the probability as, $\dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$, and here the favoured outcome will be equal to the sum of black balls and red balls, whereas the total outcome will be equal to the sum of number of all the balls in the bag.

Complete step-by-step answer:
It is given in the question that a bag contains 4 red balls, 6 blue balls and 3 black balls. A ball is drawn from the bag at random and we have to find the probability that the ball drawn is not blue. We will first find the total outcome, which is the sum of all the balls in the bag, which is given as,
Total outcome = 4 red balls + 6 blue balls + 3 black balls = 13 balls.
Now, we will try to find the favoured outcome, which is a ball being drawn that is not blue. This means that we have to take the favoured outcome as the number of balls that are not blue. So, we can say,
Favoured outcome = 4 red balls + 3 black balls = 7 balls.
Now, we will use the formula for probability to find the probability of a blue ball not being drawn. So,
Probability = $\dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}=\dfrac{7}{13}$.
Therefore, the probability that the ball drawn is not blue is $\dfrac{7}{13}$.
Hence, the correct answer is option C.

Note: It is observed that many students make a mistake in reading the question and they miss to read the word ‘not’ as a result of which they find the probability of a ball being drawn that is blue, which would be $\dfrac{6}{13}$, and as it is given in the option, the students will take it as correct answer. This would be incorrect as the correct answer is $\dfrac{7}{13}$. So, the students must read the question carefully before solving.