A bag contains 6 red, 5 black and 4 white balls.

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A bag contains 6 red, 5 black, and 4 white balls. A 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.

Solution:

Total number of balls = 6 + 5 + 4 = 15
Number of red balls = 6
Number of black balls = 5
Number of white balls = 4
(i) Probability of a white ball will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome } = \\ \frac { 4 }{ 15 }
(ii) Probability of red ball will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome } = \\ \frac { 6 }{ 15 } = \\ \frac { 2 }{ 5 }
(iii) Probability of not black ball will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 15-5 }{ 15 }
= \\ \frac { 10 }{ 15 }
= \\ \frac { 2 }{ 3 }
(iv) Probability of red or white ball will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 6+4 }{ 15 }
= \\ \frac { 10 }{ 15 }
= \\ \frac { 2 }{ 3 }

A bag contains 5 red, 8 white and 7 black balls. A ball is drawn from the bag at random. Find the probability that the drawn ball is:
(i) red or white
(ii) not black
(iii) neither white nor black

Solution:

Total number of balls in a bag = 5 + 8 + 7 = 20
(i) Number of red or white balls = 5 + 8 = 13
Probability of red or white ball will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome } = \\ \frac { 13 }{ 20 }
(ii) Number of ball which are not black = 20 – 7 = 13
Probability of not black ball will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome } = \\ \frac { 13 }{ 20 }
(iii) Number of ball which are neither white nor black
= Number of ball which are only red = 5
Probability of neither white nor black ball will be
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 5 }{ 20 }
= \\ \frac { 1 }{ 4 }

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