A boy has a collection of balls of different colours. He has a total of 35 balls in his basket out of which seven are black in colour and eight are yellow in colour. Out of remaining balls, some are white and the rest are red. Based on the above, answer the following questions: (a) If the probability of drawing a red ball at random from the basket is three times that of a white ball, then find the number of red balls in the basket. (b) Find the probability of drawing a ball at random from the basket which is either a black or a white ball.

 A boy  has a collection of balls of different colours. He has a total of 35 balls in his basket out of which seven are black in colour and eight are yellow in colour. Out of remaining balls, some are white and the rest are red.

Based on the above, answer the following questions:

(a) If the probability of drawing a red ball at random from the basket is three times that of a white ball, then find the number of red balls in the basket.

(b) Find the probability of drawing a ball at random from the basket which is either a black or a white ball

Total balls = 35

Number of Black balls = 7

Number of Yellow balls = 8

Remaining balls = 35 − 7 − 8 = 20  

Let number of white balls = w

Let number of red balls = r 

Given that 

Out of remaining balls, some are white and the rest are red.

Remaining balls =  20  

w + r  =  20  ---------[1]

Given 

P(red) = 3 × P(white) 

 P(red) = r/35

P(white) = w/35 

 r/35 = 3 × w/35

r = 3w  ---------(2) 

 Put (2) in (1)

w + r  =  20

w + 3w = 20

4w = 20

w = 5  

use r = 3w 

 r = 3 × 5 = 15 

 Number of red balls = 15

Number of  Black balls = 7

Numbe r of White balls [w] = 5  

 Number of  favourable outcomes = 7 + 5 = 12  

P(black or white) = 12/35

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