Probability with Explanation

Q8. A box contains 10 red and 10 yellow balls. The probability of drawing two balls of the same color, is:

A. 10 19	B. 5 19
C. 9 19	D. 9 38

Answer- Option C

Explanation-

Total number of balls = 20.
Let S be the sample space. Then,
n(S) = Number of ways of drawing 2 balls out of 20 = ²⁰C₂
=

20 x 19 2 x 1

= 190.

Let E = event of drawing 2 balls of the same color.
n(E) = (¹⁰C₂ + ¹⁰C₂) = 2 x

10 x 9 2 x 1

= 90

.

P(E) =

n(E) n(S)

=

90 190

=

9 19

.

Q9. In class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

A. 21 46	B. 3 25
C. 25 117	D. 1 50

Answer- Option A

Explanation-

Let S be the sample space and E be the event of slecting 1 girl and 2 boys. Then,
n(S) = Number of ways of selecting 3 students out of 25 = ²⁵C₃
=

25 x 24 x 23 3 x 2 x 1

= 2300.

n(E) = (¹⁰C₁ + ¹⁵C₂) = 10 x

15 x 14 2 x 1

= 1050.

P(E) =

n(E) n(S)

=

1050 2300

=

21 46

.

Q10. Rohan and his wife appear in an interview for two vacancies in the same post. The probability of husband's selection is

1 7

1 5

A. 8 15	B. 2 7
C. 4 7	D. 4 5

Answer- Option B

Explanation-

Let A = Event that the husband is selected
and B = Event that ihe wife is selected.
Then, P(A) =

1 7

P(B) =

1 5

.

P(‾A) =

1 -

1 7

=

6 7

and P(‾B) =

1 -

1 5

=

4 5

.

Required probability = P [(A and not B) or (B and not A)]
= P[(A and ‾B) or (B and ‾A)]
= P(A and ‾B) + P(B and ‾A)
= P(A).P(‾B) + P(B).P(‾A) =

1 7

x

4 5

+

1 5

x

6 7

=

2 7

Q11. Two dice are thrown together. What is the probability that the sum of the numbers on the two faces is divisible by 4 or 6?

A. 1 12	B. 1 3
C. 7 15	D. 7 18

Answer- Option D

Explanation-

Clearly, n(S) = 6 x 6 = 36.
Let E be the event that the sum of the numbers on the two faces is divisible by 4 or 6. Then
E = {(1, 3), (1, 5), (2, 2), (2, 4), (2, 6), (3, 1), (3, 3), (3, 5), (4, 2), (4, 4), (5, 1), (5, 3), (6, 2), (6, 6)}
n(E) = 14. Hence, P(E) =

n(E) n(S)

=

14 36

=

7 18

.

Q12. An unbiased die is tossed. Find the probability of getting a multiple of 3.

A. 1 3	B. 1 7
C. 1 5	D. 2 5

Answer- Option A

Explanation-

Here S = {1, 2, 3, 4, 5, 6}.
Let E be the event of getting a multiple of 3.
Then, E = {3, 6}.
Hence, P(E) =

n(E) n(S)

=

2 6

=

1 3

.

Q13. In a throw of a coin. Find the probability of getting a head?

A. 1 5	B. 1 7
C. 1 2	D. 1 8

Answer- Option C

Explanation-

Here S = {H, T} and E = {H}.
P(E) =

n(E) n(S)

=

1 2

.

Q14. In a simultaneous throw of a pair of dice, find the probability of getting a total more than 7.

A. 8 7	B. 5 12
C. 7 18	D. 5 9

Answer- Option B

Explanation-

Here, n(S) = {6 x 6} = 36.
Let E = Event of getting a total more than 7
= {(2,6), (3,5), (3,6),(4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,2),(6,3), (6,4), (6,5), (6,6)}.
P(E) =

n(E) n(S)

=

15 36

=

5 12

.