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1. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the

probability that the ticket drawn has a number which is a multiple of 3 or 5?

1

2

A.

B.

2

5

8

9

C.

D.

15

20

**Answer:** Option **D**

**Explanation:**

Here, S = {1, 2, 3, 4, ...., 19, 20}.

Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.

*n*(E) 9

P(E) =

= .

*n*(S) 20

2. A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the

probability that none of the balls drawn is blue?

10

11

A.

B.

21

21

2

5

C.

D.

7

7

**Answer:** Option **A **

**Explanation:**

Total number of balls = (2 + 3 + 2) = 7.

Let S be the sample space.

Then,*n*(S) = Number of ways of drawing 2 balls out of 7

= 7C

2

(7 x 6)

=

(2 x 1)

= 21.

Let E = Event of drawing 2 balls, none of which is blue.

*n*(E) = Number of ways of drawing 2 balls out of (2 + 3) balls.

= 5C

2

= (5 x 4)

(2 x 1)

= 10.

*n*(E) 10

P(E) =

= .

*n*(S) 21

3. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the

probability that it is neither red nor green?

1

3

A.

B.

3

4

7

8

C.

D.

19

21

9

E. 21

**Answer:** Option **A**

**Explanation:**

Total number of balls = (8 + 7 + 6) = 21.

Let E = event that the ball drawn is neither red nor green

= event that the ball drawn is blue.

*n*(E) = 7.

*n*(E) 7 1

P(E) =

= = .

*n*(S) 21 3

4. What is the probability of getting a sum 9 from two throws of a dice?

1

1

A.

B.

6

8

1

1

C.

D.

9

12

**Answer:** Option **C**

**Explanation:**

In two throws of a die,*n*(S) = (6 x 6) = 36.

Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.

*n*(E) 4 1

P(E) =

= = .

*n*(S) 36 9

5. Three unbiased coins are tossed. What is the probability of getting at most two heads?

3

1

A.

B.

4

4

3

7

C.

D.

8

8

**Answer:** Option **D**

**Explanation:**

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

Let E = event of getting at most two heads.

Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.

*n*(E) 7

P(E) =

= .

*n*(S) 8

probability that the ticket drawn has a number which is a multiple of 3 or 5?

1

2

A.

B.

2

5

8

9

C.

D.

15

20

Here, S = {1, 2, 3, 4, ...., 19, 20}.

Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.

P(E) =

= .

2. A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the

probability that none of the balls drawn is blue?

10

11

A.

B.

21

21

2

5

C.

D.

7

7

Total number of balls = (2 + 3 + 2) = 7.

Let S be the sample space.

Then,

= 7C

2

(7 x 6)

=

(2 x 1)

= 21.

Let E = Event of drawing 2 balls, none of which is blue.

= 5C

2

= (5 x 4)

(2 x 1)

= 10.

P(E) =

= .

3. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the

probability that it is neither red nor green?

1

3

A.

B.

3

4

7

8

C.

D.

19

21

9

E. 21

Total number of balls = (8 + 7 + 6) = 21.

Let E = event that the ball drawn is neither red nor green

= event that the ball drawn is blue.

P(E) =

= = .

4. What is the probability of getting a sum 9 from two throws of a dice?

1

1

A.

B.

6

8

1

1

C.

D.

9

12

In two throws of a die,

Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.

P(E) =

= = .

5. Three unbiased coins are tossed. What is the probability of getting at most two heads?

3

1

A.

B.

4

4

3

7

C.

D.

8

8

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

Let E = event of getting at most two heads.

Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.

P(E) =

= .

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