Question

There are two bags, one containing 4 red and 5, blue balls and the other containing 6 black and
2 white balls. One ball from each bag is taken out. What is the probability that the balls are
(i) red and black
(ii) blue and white
(iii), red and white
(iv) blue and black.
[HOTS]​

Answer 1

(i) The probability that the balls are red and black is 1 / 3.

(ii) The probability that the balls are blue and white is 5 / 36.

(iii) The probability that the balls are red and white is 1 / 9.

(iv) The probability that the balls are blue and black is 5 / 12.

• Given,

Number of red balls in the first bag = 4

Number of blue balls in the same bag = 5

Number of black balls in the second bag = 6

Number of white balls in the same bag = 2

• Now, total number of balls in the first bag = Number of red balls + Number of balck balls

= 4 + 5 = 9

Total number of balls in the second bag = Number of blue balls + Number of white balls

= 6 + 2 = 8

• Probability of an event = Number of favourable outcomes / Total number of possible outcomes

• Therefore,

Probability of drawing a red ball (P₁) = Number of red balls in the first bag / Total number of balls in the first bag

=> P₁ = 4 / 9

Probability of drawing a blue ball (P₂) = Number of blue balls in the first bag / Total number of balls in the first bag

=> P₂ = 5 / 9

Probability of drawing a black ball (P₃) = Number of black balls in the second bag / Total number of balls in the second bag

=> P₃ = 6 / 8 = 3 / 4

Probability of drawing a white ball (P₄) = Number of white balls in the second bag / Total number of balls in the second bag

=> P₄ = 2 / 8 = 1 / 4

(i) Probability of drawing a red and a black ball = Probability of drawing a red ball × Probability of drawing a black ball

=> P₁ × P₃ = (4 / 9) × (3 / 4)

=> P₁ × P₃ = 1 / 3

(ii) Probability of drawing a blue and a white ball = Probability of drawing a blue ball × Probability of drawing a white ball

=> P₂ × P₄ = (5 / 9) × (1 / 4)

=> P₂ × P₄ = 5 / 36

(iii) Probability of drawing a red and a white ball = Probability of drawing a red ball × Probability of drawing a white ball

=> P₁ × P₄ = (4 / 9) × (1 / 4)

=> P₁ × P₄ = 1 / 9

(iv) Probability of drawing a blue and a black ball = Probability of drawing a blue ball × Probability of drawing a black ball

=> P₂ × P₃ = (5 / 9) × (3 / 4)

=> P₂ × P₃ = 5 / 12