EduSahara™ Worksheet

Question 1

1.

On a particular day, at a crossing in a city, the various types of 100 vehicles going past during a time-interval were observed as under:

Type of Vehicle

Two-wheeler

Four-wheeler

Three-wheeler

Frequency

25

35

40

Out of these vehicles, if one is choosen at random, what is the probability that the choosen vehicle is a 'Two-wheeler' ?

(i)

1
4
(ii)

2
5
(iii)

1
2
(iv)

3
4
(v)

0

Question 2

2.

The following table shows the blood-groups of 351 students of a class.

Blood group

AB

O

B

A

Number of students

54

72

81

144

One student of the class is choosen at random. What is the probability that the choosen student has blood group 'A' ?

(i)

17
39
(ii)

23
39
(iii)

16
39
(iv)

5
13
(v)

17
40

Question 3

3.

A bag contains 30 white marbles, 8 red marbles, 14 pink marbles and 18 yellow marbles. One marble is drawn at random from the bag. Find the probability that the marble drawn is white.

(i)

3
7
(ii)

1
2
(iii)

2
7
(iv)

4
7

Question 4

4.

A box contains 18 white marbles, 22 black marbles, 6 orange marbles and 18 red marbles. One marble is drawn at random from the box. Find the probability that the marble drawn is not orange.

(i)

7
8
(ii)

10
11
(iii)

15
16
(iv)

3
32
(v)

29
32

Question 5

5.

A box contains 44 white balls, 60 orange balls, 32 blue balls and 12 black balls. One ball is drawn at random from the box. Find the probability that the ball drawn is orange or black.

(i)

17
37
(ii)

18
37
(iii)

19
37
(iv)

1
2

Question 6

6.

A bag contains 32 blue marbles, 12 gray marbles, 16 black marbles and 4 orange marbles. One marble is drawn at random from the bag. Find the probability that the marble drawn is neither orange nor blue.

(i)

3
8
(ii)

7
16
(iii)

9
16
(iv)

8
17
(v)

1
2

Question 7

7.

What is the probability of a sure event?

(i)

3
4
(ii)

0
(iii)

1
(iv)

1
2
(v)

1
4

Question 8

8.

What is the probability of an impossible event?

(i)

1
4
(ii)

3
4
(iii)

1
2
(iv)

0
(v)

1

Question 9

9.

There are 58 students in a class room of whom 32 are boys and 26 are girls. From these students, one is choosen at random. What is the probability that the choosen student is a boy ?

(i)

13
29
(ii)

17
29
(iii)

15
29
(iv)

17
30
(v)

16
29

Question 10

10.

There are 50 students in a class room of whom 22 are boys and 28 are girls. From these students, one is choosen at random. What is the probability that the choosen student is a girl ?

(i)

3
5
(ii)

11
25
(iii)

15
26
(iv)

13
25
(v)

14
25

Question 11

11.

In a lottery, there are 25 prizes and 20 blanks. What is the probability of getting a prize?

(i)

4
9
(ii)

5
9
(iii)

3
5
(iv)

2
3

Question 12

12.

In a lottery, there are 15 prizes and 18 blanks. What is the probability of not getting a prize?

(i)

7
11
(ii)

7
12
(iii)

5
11
(iv)

6
11

Question 13

13.

Which of the following are true?

a)	Probability of getting 110 marks out of 100 is 1.1
b)	The probability of an event that cannot happen is unknown
c)	If the probability is too less, it will become negative
d)	If the probability of failing the exam is 0.88, the probability of passing the exam is 0.12
e)	The probability of an event that is very likely to happen is 1

(i)

{b,d}
(ii)

{d}
(iii)

{c,e,d}
(iv)

{a,d}

Question 14

14.

Which of the following experiments have equally likely outcomes?

a)	A ball is hit. It reaches the boundary or not
b)	A man starts his vehicle. It starts or it does not starts
c)	A baby is born. It is a boy or girl
d)	A true/false question is attempted. The answer is either right or wrong
e)	A man throws a die. The number on the top is either 6 or not 6

(i)

{c,d}
(ii)

{b,d,c}
(iii)

{b,d}
(iv)

{a,c}
(v)

{e,a,c}

Question 15

15.

Which of the following are possible values of probability?

a)

5

3

b)

0.57

c)

-3

d)

3

8

e)

5

(i)

{a,b}
(ii)

{c,d}
(iii)

{b,d}
(iv)

{c,d,b}
(v)

{e,a,b}

Question 16

16.

If P(E) =
0.8
, find P(
E
)

(i)

2.2
(ii)

0.2
(iii)

8.2
(iv)

1.2
(v)

7.2

Question 17

17.

Which of the following are true?

a)	The probability of an unsure event is 0
b)	The probability of an imposible event can be > 1
c)	The probability of an impossible event is 1
d)	The probability of a sure event is 1
e)	For an event E, we have 0 ≤ P(E) ≤ 1

(i)

{b,e}
(ii)

{d,e}
(iii)

{a,d}
(iv)

{c,a,d}
(v)

{b,e,d}

Question 18

18.

Which of the following are true?

a)

P(E) = 1 - P(
E
)

b)

P(E) + P(not E) = 1

c)

P(E) - P(not E) = 0

d)

P(E) + P(
E
) = 0

e)

P(E) - P(
E
) = 0

(i)

{d,b}
(ii)

{e,c,a}
(iii)

{a,b}
(iv)

{c,a}
(v)

{d,b,a}

Question 19

19.

Two players Rita and Akshaya play a tennis match. It is known that the probability of Rita winning the match is 0.56. What is the probability of Akshaya winning the match?

(i)

6
13
(ii)

14
25
(iii)

2
5
(iv)

12
25
(v)

11
25

Question 20

20.

A die is thrown 530 times. The number 4 appears on the upper face 68 times. Now the die is thrown at random. What is the probability of getting a 4 ?

(i)

7
53
(ii)

5
38
(iii)

33
265
(iv)

231
265
(v)

34
265

Question 21

21.

243 families with 2 children were selected randomly, and the following data were recorded

No. of girls in a family

0

1

2

Number of families

63

72

108

Compute the probability of the family, chosen at random, having no girls.

(i)

8
27
(ii)

2
7
(iii)

20
27
(iv)

2
9
(v)

7
27

Question 22

22.

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes :

Outcome

3 heads

2 heads

1 heads

No heads

Frequency

30

45

55

70

If the three coins are simultaneously tossed again, compute the probability of '2 heads' coming up.

(i)

1
5
(ii)

10
41
(iii)

9
40
(iv)

31
40
(v)

1
4

Question 23

23.

A die is thrown 385 times with the frequencies for outcomes 1, 2, 3, 4, 5 and 6 as given in the following table

Outcome

1

2

3

4

5

6

Frequency

45

50

60

65

80

85

If the die is thrown again randomly, find the probability of getting 4 as outcome.

(i)

64
77
(ii)

12
77
(iii)

7
39
(iv)

13
77
(v)

2
11

Question 24

24.

The distances (in km) of engineers from their residence to their place of work were found as follows

29

10

19

18

24

18

11

12

7

22

16

What is the empirical probability that an engineer lives less than 12 km from her place of work?

(i)

1
3
(ii)

4
11
(iii)

2
11
(iv)

8
11
(v)

3
11

Question 25

25.

The distances (in km) of engineers from their residence to their place of work were found as follows

19

29

5

18

1

7

19

16

12

What is the empirical probability that an engineer lives greater than 5 km from her place of work?

(i)

7
9
(ii)

2
3
(iii)

4
5
(iv)

8
9
(v)

2
9

Question 26

26.

Manisha and Vimala are friends. What is the probability that both will have different birthdays? (ignoring a leap year).

(i)

1
365
(ii)

1
(iii)

365
366
(iv)

363
365
(v)

364
365

Question 27

27.

Sujatha and Sarojini are friends. What is the probability that both will have same birthdays? (ignoring a leap year).

(i)

364
365
(ii)

2
365
(iii)

1
365
(iv)

1
183
(v)

0

Question 28

28.

In a musical chair game, the person playing the music has been advised to stop playing the music at any time with in 2 minutes after she starts playing. What is the probabilty that the music will stop within the first half-minute after starting?

(i)

2
5
(ii)

1
2
(iii)

0
(iv)

1
4
(v)

3
4

Question 29

29.

A carton consist of 88 shirts of which 76 are good, 7 have minor defects and 5 have major defects. Rajesh, a trader, will only accept the shirts which are good, but Aruna, another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. What is the probability that it is acceptable to Rajesh?

(i)

3
22
(ii)

9
11
(iii)

19
22
(iv)

10
11
(v)

20
23

Question 30

30.

A carton consist of 87 shirts of which 74 are good, 12 have minor defects and 1 have major defects. Venkat, a trader, will only accept the shirts which are good, but Sujatha, another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. What is the probability that it is acceptable to Sujatha?

(i)

1
(ii)

87
88
(iii)

1
87
(iv)

85
87
(v)

86
87

Question 31

31.

A lot of 28 bulbs contain 13 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective ?

(i)

3
7
(ii)

14
29
(iii)

1
2
(iv)

13
28
(v)

15
28

Question 32

32.

A lot of 30 bulbs contain 18 defective ones. One bulb is drawn at random from the lot. Suppose the bulb drawn is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective ?

(i)

18
29
(ii)

10
29
(iii)

2
5
(iv)

11
29
(v)

12
29

Question 33

33.

A box contains 70 discs which are numbered from 1 to 70. If one disc is drawn at random from the box, find the probability that it bears a two-digit number.

(i)

61
70
(ii)

6
7
(iii)

9
70
(iv)

31
35
(v)

62
71

Question 34

34.

A box contains 50 discs which are numbered from 1 to 50. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.

(i)

7
50
(ii)

4
25
(iii)

43
50
(iv)

8
51
(v)

3
25

Question 35

35.

A box contains 50 discs which are numbered from 1 to 50. If one disc is drawn at random from the box, find the probability that it bears a number divisible by 5.

(i)

1
5
(ii)

4
5
(iii)

2
5
(iv)

1
3
(v)

0

Question 36

36.

A game consists of tossing a coin 3 times and noting its outcome each time. Santosh wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Santosh will lose the game.

(i)

3
4
(ii)

4
5
(iii)

1
4
(iv)

1
(v)

1
2

Question 37

37.

66 cards are numbered 1,2,3,....66 and put in a box and mixed thoroughly. A card is drawn at random. What is the probability that the number on the drawn card is an odd number?

(i)

5
6
(ii)

4
5
(iii)

1
2
(iv)

2
3
(v)

3
4

Question 38

38.

58 cards are numbered 1,2,3,....58 and put in a box and mixed thoroughly. A card is drawn at random. What is the probability that the number on the drawn card is a prime number?

(i)

21
29
(ii)

3
10
(iii)

7
29
(iv)

9
29
(v)

8
29

Question 39

39.

79 cards are numbered 1,2,3,....79 and put in a box and mixed thoroughly. A card is drawn at random. What is the probability that the number on the drawn card is divisible by 5?

(i)

64
79
(ii)

1
5
(iii)

16
79
(iv)

14
79
(v)

15
79

Question 40

40.

96 cards are numbered 1,2,3,....96 and put in a box and mixed thoroughly. A card is drawn at random. What is the probability that the number on the drawn card is less then 30?

(i)

67
96
(ii)

7
24
(iii)

29
96
(iv)

5
16
(v)

30
97

Question 41

41.

88 cards are numbered 1,2,3,....88 and put in a box and mixed thoroughly. A card is drawn at random. What is the probability that the number on the drawn card is greater then 26?

(i)

13
44
(ii)

31
44
(iii)

32
45
(iv)

8
11
(v)

15
22

Question 42

42.

Suppose a die is thrown on a rectangular region as shown below. What is the probability that it will land inside the circle of diameter 12.00 cm?

(i)

45
133
(ii)

43
133
(iii)

89
133
(iv)

44
133
(v)

45
134

Question 43

43.

A missing helicopter is reported to have crashed somewhere in the rectangular region shown in fig. What is the probability that it crashed inside the shaded region as shown in the figure?

(i)

0
(ii)

1
4
(iii)

1
2
(iv)

3
4
(v)

2
5

Assignment Key