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A bag contains 4 red, 5 black and 6 white balls. One ball is drawn from the bag at random. Find the probability that the ball drawn is:

(i) white

(ii) red

(iii) not black

(iv)red or white

Answer:

(i) White

Total numbers of red balls = 4 Number of black balls = 5 Number of white balls = 6

Total number of balls = 4 + 5 + 6 = 15

Probability of getting a white ball is = Total number of white balls/Total number of balls

= 6/15

= 2/5

∴ Probability of getting a white ball is 2/5

(ii) Red

Total numbers of red balls = 4 Number of black balls = 5 Number of white balls = 6

Total number of balls = 4 + 5 + 6 = 15

Probability of getting a red ball is = Total number of red balls/Total number of balls

= 4/15

∴ Probability of getting a white ball is 4/15

(iii) Not black

Total numbers of red balls = 4 Number of black balls = 5 Number of white balls = 6

Total number of balls = 4 + 5 + 6 = 15

Number of non-black balls = 4 + 6 = 10

Probability of getting a non-black ball is = Total number of non-black balls/Total number of balls

= 10/15

= 2/3

∴ Probability of getting a non-black ball is 2/3

(iv) Red or white

Total numbers of red balls = 4 Number of black balls = 5 Number of white balls = 6

Total number of balls = 4 + 5 + 6 = 15 Number of red and white balls = 4 + 6 = 10

Probability of getting a red or white ball is = Total number of red or white balls/Total number of balls

= 10/15

= 2/3

∴ Probability of getting a red or white ball is 2/3

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