A bag contains 3 red balls, 5 black balls and 4 white balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is:

Total number of possible outcomes = 12 {3 red balls, 5 black balls & 4 white balls}

(i) E ⟶ event of getting white ball

No. of favourable outcomes = 4 {4 white balls}

Probability, P(E) = 4/12 = 1/3

(ii) E ⟶ event of getting red ball

No. of favourable outcomes = 5 {3 red balls}

P (E) = 3/12 = 1/4

(iii) E ⟶ event of getting black ball

No. of favourable outcomes = 5 {5 black balls}

P (E) = 5/12

(iv) E ⟶ event of getting red

No. of favourable outcomes = 3 {3 black balls}

P(E) = 3/12 = 1/4

(Bar E) ⟶ event of not getting red.

P(Bar E) = 1 – P(E)

= 1 – 1/4

= 3/4

Given: A bag contains 3 red, 5 black and 4 white balls

Required to find: Probability of getting a

(i) White ball

(ii) Red ball

(iii) Black ball

(iv) Not red ball

Total number of balls 3 + 5 + 4 =12

(i) Total number of white balls is 4

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting a white ball = 4/12 = 1/3

(ii) Total number red balls are 3

We know that Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting a red ball = 3/12 = 1/4

(iii) Total number of black balls is 5

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting a black ball = 5/12

(iv) Total number of balls which are not red are 4 white balls and 5 black balls i.e. 4 + 5 = 9

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting no red ball = 9/12 = 3/4