# Examples(Set 2) - Probability

6. A dice is thrown. What is the probability that the number shown in the dice is divisible by
2
?

A.
1/
6

B.
1/
3

C.
1/
2

D.
1/
4

Explanation:

The possible outcomes when a die thrown is {1,2,3,4,5,6}.

Therefore, the number of possible outcomes of a die is 6.

i.e., n(S) = 6

E = Event that the number shown in the dice is divisible by 2

= {2,4,6}

n(E) = 3

P(E) = n(E)/ n(S)

= 3/ 6

= 1/ 2

7.Doramon draws a card from a pack of cards. What is the probability that the card drawn is a card of red suit?

A. None of these

B.
1/
4

C.
1/
2

D.
3/
4

Explanation:

Total number of cards, n(S) = 52

Total number of red cards, n(E) = 26

P(E) = n(E)/ n(S)

= 26/ 52

= 1/ 2

8. There are
15
boys and
10
girls in a class. If three students are selected at random, what is the probability that
1
girl and
2
boys are selected?

A.
21/
46

B.
1/
2

C.
1/
40

D.
7/
42

Explanation:

n(S) = Total number of ways of selecting 3 students from 25 students

= 25 C 3

n(E) = Number of ways of selecting 1 girl and 2 boys from 10 girls and 15 boys

n(E) = 15 C 2 × 10 C 1

P(E) = n(E)/ n(S)

=

__(15C2 × 10C1)__

25 C 3

= 21/ 46

9.One card is randomly drawn from a pack of
52
cards. What is the probability that the card drawn is a face card(Jack, Queen or King)

A.
1/
13

B.
3/
13

C.
4/
13

D.
2/
13

Explanation:

Total number of cards, n(S) = 52

Total number of face cards, n(E) = 12

P(E) = n(E)/ n(S)

= 12/ 52

= 3/ 13

10.
3
balls are drawn randomly from a bag contains
3
black,
5
red and
4
blue balls. What is the probability that the balls drawn contain balls of different colors?

A.
3/
11

B.
1/
3

C.
1/
2

D.
2/
11

Explanation:

Total number of balls

=3 + 5 + 4 = 12

Let S be the sample space.

n(S) =Total number of ways of drawing 3 balls out of 12 = 12 C 3

n(E) =drawing 3 different coloured balls.

=one black ball from 3 black balls, one red ball from 5 red balls, one blue ball from 4 blue balls.

= 3 C 1 × 5 C 1 × 4 C 1

P(E) = n(E)/ n(S)

=

__(3 C 1 × 5 C 1 × 4 C 1)__

12 C 3

=

__3 × 5 × 4__

( 12 × 11 × 10 /3 × 2 × 1 )

= 3/ 11