# Examples(Set 1) - Probability

1. What is the probability of getting a number less than
4
when a die is rolled?

A.
1/
2

B.
1/
6

C.
1/
3

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

Now, if we get a 4 on rolling die then the number of favourable outcome E = { 1 , 2 , 3 }

Hence, n(E) = 3

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

= 3/ 6

= 1/ 2

2.When tossing two coins once, what is the probability of tails on both the coins?

A. None of these

B.
1/
4

C.
1/
2

D.
3/
4

Explanation:

total number of outcomes possible when two coins are tossed

S = {HH, HT, TH, TT}

n(S)=4

E = event of getting tails on both the coins = {TT}

n(E) = 1

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

= 1/ 4

3. Three coins are tossed. What is the probability of getting atleast two tails?

A.
1/
2

B.
7/
8

C.
1/
8

D.
1/
7

Explanation:

S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}

n(S) = 8 E = event of getting atleast two Tails = {TTT, TTH, THT, HTT}

Hence, n(E) = 4

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

= 4/ 8

=1/2

4.A die is rolled twice. What is the probability of getting a sum equal to
8
?

A.
2/
3

B.
1/
9

C.
1/
6

D.
1/
3

Explanation:

total number of outcomes possible when a die is rolled twice

n(S) = 6 × 6 = 36

E = Getting a sum of 8 when the two dice fall = { ( 2 , 6 ), ( 3 , 5 ) , ( 4 , 4 ) , ( 4 , 4 ) , ( 5 , 3 ), ( 6 , 2 ) }

Hence, n(E) = 6

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

= 6/ 36

= 1/ 6

5. A bag contains
2
yellow,
3
green and
2
blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

A.
10/
21

B.
9/
11

C.
1/
2

D.
7/
11

Explanation:

Total number of balls

= 2 + 3 + 2 = 7

Let S be the sample space.

n(S) = 7 C 2

n(E) = Number of ways of drawing 2 balls , none of them is blue = Number of ways of drawing 2 balls from the total 5

=5 C 2

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

= 5 C 2/ 7 C 2

=

__( 5 × 4/ 2 × 1 )__

( 7 × 6/ 2 × 1 )

= 10/ 21