A bag contains 5 red, 8 white and 7 black balls. A ball is drawn from the bag at random. Find the probability that the drawn ball is

(i) red or white

(ii) not black

(iii) neither white nor black.

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 + 8 + 7 = 20.

So, the sample space of the experiment has 20 equally likely outcomes.

(i) Let E₁ be the event 'a red or white ball is drawn'.

The number of red or white balls = 5 + 8 = 13.

So, the number of favourable outcomes to the E₁ = 13.

∴ P(E₁) = P(a red or white ball) = $\dfrac{13}{20}.$

Hence, the probability that the ball drawn is red or white is $\dfrac{13}{20}.$

(ii) Drawing a not black ball means drawing a red or white ball.

∴ P(not black ball) = P(a red or white ball) = $\dfrac{13}{20}.$

Hence, the probability that the ball drawn is not a black ball is $\dfrac{13}{20}.$

(iii) If a ball drawn is neither white nor black it means a red ball is drawn.

No. of red balls = 5.

∴ P(a red ball is drawn) = $\dfrac{5}{20} = \dfrac{1}{4}.$

Hence, the probability that a red ball is drawn is $\dfrac{1}{4}.$