A bag contains 5 white balls, 7 red balls, 4 black balls and 2 blue balls. One ball is drawn at random from the bag. What is the probability that the ball drawn is :
(i) white or blue
(ii) red or black
(iii) not white
(iv) neither white nor black?

Question

A bag contains 5 white balls, 7 red balls, 4 black balls and 2 blue balls. One ball is drawn at random from the bag. What is the probability that the ball drawn is :
(i) white or blue
(ii) red or black
(iii) not white
(iv) neither white nor black?

KnowledgeBoat · Accepted Answer

Since, a ball is drawn at random from the bag, so all the balls are equally likely to be drawn. Total number of balls in the bag = 5 + 7 + 4 + 2 = 18. So, the sample space of the experiment has 18 equally likely outcomes. (i) Let E₁ be the event 'a white or blue ball is drawn'. The number of white or blue balls = 5 + 2 = 7. So, the number of favourable outcomes to the E₁ = 7. ∴ P(E₁) = P(a white or blue ball) = Hence, the probability that the ball drawn is white or blue is (ii) Let E₂ be the event 'a red or black ball is drawn'. The number of red or black balls = 7 + 4 = 11. So, the number of favourable outcomes to the E₂ = 11. ∴ P(E₂) = P(a red or black ball) = Hence, the probability that the ball drawn is red or black is (iii) Let E₃ be the event 'not white ball is drawn'. Probability of not white ball drawn = Probability of any other ball drawn. No. of balls except white balls = 18 - 5 = 13. So, the number of favourable outcomes to the E₃ = 13. ∴ P(E₃) = P(not a white ball) = Hence, the probability that the ball drawn is not white is (iv) Let E₄ be the event 'neither white nor black ball is drawn'. Probability that neither white nor black ball is drawn = Probability of a red or blue ball drawn. No. of red or blue balls = 7 + 2 = 9. So, the number of favourable outcomes to the E₄ = 9. ∴ P(E₄) = Hence, the probability that the ball drawn is neither white nor black is

Mathematics

A bag contains 5 white balls, 7 red balls, 4 black balls and 2 blue balls. One ball is drawn at random from the bag. What is the probability that the ball drawn is :
(i) white or blue
(ii) red or black
(iii) not white
(iv) neither white nor black?

Probability

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