# Examples(Set 3) - Probability

11. 4
coins are tossed together. What is the probability of getting exactly
2
heads
?

A.
1/4

B.
1/
3

C.
3/8

D.
1/
8

Total number of outcomes possible when a coin is tossed = 2 (∵ Head or Tail)

Hence, total number of outcomes possible when 4 coins are tossed, n(S)

=24

n(E) = Number of ways of getting exactly 2 heads when 4 coins are tossed

= 4 C 2

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

=

__4 C 2__

24

= 3/8

12.What is the probability of drawing a "King" from a deck of
52
cards?

A. None of these

B.
1/
4

C.
1/
2

D.
3/
4

Explanation:

Total number of cards, n(S) = 52

Total number of 'King" cards, n(E) = 4

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

= 4/ 52

= 1/ 4

13. What is the probability of selecting a prime number from
1
,
2
,
3
,
⋯
15
?

A.
7/15

B.
6/14

C.
1/3

D.
6/15

Explanation:

Total count of numbers, n(S) = 15

Prime numbers in the given range are { 2 , 3 , 5 , 7, 11, 13}

n(E) = 6

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

= 6/ 15

13.One card is randomly drawn from a pack of
52
cards. What is the probability that the card drawn is a daimond card

A.
1/
4

B.
1/2

C.
1/3

D.
1/8

Explanation:

Total number of cards, n(S) = 52

Total number of daimond cards, n(E) = 13

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

= 13/ 52

= 1/4

15.
A bag contains
4
black,
5
yellow and
6
green balls. Three balls are drawn at random from the bag. What is the probability that all of them are yellow?

A.
2/
81

B.
2/
91

C.
1/
81

D.
1/
8

Explanation:

Total number of balls

=4 + 5 + 6 = 15

Let S be the sample space.

n(S) = Total number of ways of drawing 3 balls out of 15

= 15 C 3

n(E) = Number of ways of drawing 3 balls from the total 5

= 5 C 3

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

=

__(5 C 3 )__

15 C 3

=

__(5 x 4 x 3/ 3 x 2x 1)__

( 15 × 14 × 13/ 3 × 2 × 1 )

= 2/ 91