A bag contains 8 red, 4 white and 3 black balls. One ball is drawn at random. What is the probability that the ball drawn is:

(i) white?

(ii) red or white?

(iii) neither red nor white?

(iv) not red?

Given,

Total number of outcomes = 15

(i) Let A be the event of getting white ball, then

∴ The number of favourable outcomes to the event A = 4

∴ P(A) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{4}{15}$

Hence, the probability of getting white ball is $\dfrac{4}{15}$.

(ii) Let B be the event of getting white or red ball, then

∴ The number of favourable outcomes to the event B = 12(white + red balls)

∴ P(B) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{12}{15}= \dfrac{4}{5}$

Hence, the probability of getting white or red ball is $\dfrac{4}{5}$.

(iii) Let C be the event of getting neither red nor white ball, then

∴ The number of favourable outcomes to the event C = 3 (black balls)

∴ P(C) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{3}{15}= \dfrac{1}{5}$

Hence, the probability of getting neither red nor white ball is $\dfrac{1}{5}$.

(iv) Let D be the event of not getting red ball, then

∴ The number of favourable outcomes to the event D = 7(white + black balls)

∴ P(D) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{7}{15}$

Hence, the probability of not getting red ball is $\dfrac{7}{15}$.