What is the probability that the ball drawn is

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A bag contains 3 red balls and 5 black balls. A ball is drawn at random’ from in bag. What is the probability that the ball drawn is?
(i) red?
(ii) not red?

Solution:

Number of red balls = 3
Number of black balls = 5
Total balls = 3 + 5 = 8
Let P (E) be the probability of red balls,
then P (\overline { E } ) will be the probability of not red balls.
P (E) + P (\overline { E } ) = 1
(i) But P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 3 }{ 8 }
(ii) P (\overline { E } ) = 1 – P(E)
= 1- \frac { 6 }{ 11 }
= \\ \frac { 8-3 }{ 8 }
= \\ \frac { 5 }{ 8 }

There are 40 students in Class X of a school of which 25 are girls and the. others are boys. The class teacher has to select one student as a class representative. She writes the name of each student on a separate card, the cards being identical. Then she puts cards in a bag and stirs them thoroughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of
(i) a girl?
(ii) a boy?

Solution:

Number of total students = 40
Number of girls = 25
Number of boys = 40 – 25 = 15
(i) Probability of a girl
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 25 }{ 40 }
= \\ \frac { 5 }{ 8 }
(ii) Probability of a boy
P(E) = \frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }
= \\ \frac { 15 }{ 40 }
= \\ \frac { 3 }{ 8 }

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