EduSahara™ Worksheet

Question 1

1.

On a particular day, at a crossing in a city, the various types of 155 vehicles going past during a time-interval were observed as under:

Type of Vehicle

Four-wheeler

Three-wheeler

Two-wheeler

Frequency

35

55

65

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

(i)

6
31
(ii)

7
31
(iii)

24
31
(iv)

8
31
(v)

1
4

Question 2

2.

The following table shows the blood-groups of 531 students of a class.

Blood group

A

AB

O

B

Number of students

90

117

144

180

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

(i)

16
59
(ii)

43
59
(iii)

17
60
(iv)

17
59
(v)

15
59

Question 3

3.

A bag contains 18 blue balls, 21 pink balls, 15 yellow balls and 45 red balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is yellow.

(i)

3
17
(ii)

2
11
(iii)

5
33
(iv)

28
33
(v)

4
33

Question 4

4.

A bag contains 44 white balls, 8 orange balls, 24 red balls and 16 blue balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is not orange.

(i)

2
23
(ii)

11
12
(iii)

21
23
(iv)

22
23
(v)

20
23

Question 5

5.

A box contains 52 gray marbles, 4 orange marbles, 48 yellow marbles and 44 black marbles. One marble is drawn at random from the box. Find the probability that the marble drawn is orange or gray.

(i)

13
37
(ii)

15
37
(iii)

23
37
(iv)

14
37
(v)

15
38

Question 6

6.

A bag contains 24 red balls, 48 white balls, 20 pink balls and 48 black balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is neither black nor pink.

(i)

18
35
(ii)

17
35
(iii)

19
35
(iv)

19
36

Question 7

7.

What is the probability of a sure event?

(i)

1
(ii)

3
4
(iii)

0
(iv)

1
4
(v)

1
2

Question 8

8.

What is the probability of an impossible event?

(i)

1
4
(ii)

0
(iii)

1
2
(iv)

3
4
(v)

1

Question 9

9.

There are 48 students in a class room of whom 28 are boys and 20 are girls. From these students, one is choosen at random. What is the probability that the choosen student is a boy ?

(i)

5
12
(ii)

1
2
(iii)

8
13
(iv)

7
12
(v)

2
3

Question 10

10.

There are 64 students in a class room of whom 30 are boys and 34 are girls. From these students, one is choosen at random. What is the probability that the choosen student is a girl ?

(i)

15
32
(ii)

1
2
(iii)

17
32
(iv)

6
11
(v)

9
16

Question 11

11.

In a lottery, there are 26 prizes and 18 blanks. What is the probability of getting a prize?

(i)

7
11
(ii)

6
11
(iii)

9
22
(iv)

13
22
(v)

14
23

Question 12

12.

In a lottery, there are 22 prizes and 20 blanks. What is the probability of not getting a prize?

(i)

11
21
(ii)

10
21
(iii)

1
2
(iv)

3
7

Question 13

13.

Which of the following are true?

a)	If the probability is too less, it will become negative
b)	The probability of an event that cannot happen is unknown
c)	The probability of an event that is very likely to happen is 1
d)	Probability of getting 104 marks out of 100 is 1.04
e)	If the probability of failing the exam is 0.5, the probability of passing the exam is 0.5

(i)

{a,e}
(ii)

{e}
(iii)

{b,e}
(iv)

{c,d,e}

Question 14

14.

Which of the following experiments have equally likely outcomes?

a)	A baby is born. It is a boy or girl
b)	A man throws a die. The number on the top is either 3 or not 3
c)	A ball is hit. It reaches the boundary or not
d)	A man starts his vehicle. It starts or it does not starts
e)	A true/false question is attempted. The answer is either right or wrong

(i)

{c,e,a}
(ii)

{c,e}
(iii)

{b,a}
(iv)

{a,e}
(v)

{d,b,a}

Question 15

15.

Which of the following are possible values of probability?

a)

-5.4

b)

0.2

c)

8

7

d)

4

8

e)

2

(i)

{c,d}
(ii)

{b,d}
(iii)

{c,d,b}
(iv)

{e,a,b}
(v)

{a,b}

Question 16

16.

If P(E) =
0.67
, find P(
E
)

(i)

0.33
(ii)

7.33
(iii)

8.33
(iv)

1.33
(v)

2.33

Question 17

17.

Which of the following are true?

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

(i)

{d,c,a}
(ii)

{b,a}
(iii)

{e,b,a}
(iv)

{a,c}
(v)

{d,c}

Question 18

18.

Which of the following are true?

a)

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

b)

P(E) + P(
E
) = 0

c)

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

d)

P(E) - P(
E
) = 0

e)

P(E) = 1 - P(
E
)

(i)

{b,a}
(ii)

{c,e}
(iii)

{c,e,a}
(iv)

{d,b,a}
(v)

{a,e}

Question 19

19.

Two players Priyanka and Dolly play a tennis match. It is known that the probability of Priyanka winning the match is 0.25. What is the probability of Dolly winning the match?

(i)

1
4
(ii)

1
2
(iii)

1
(iv)

4
5
(v)

3
4

Question 20

20.

A die is thrown 550 times. The number 2 appears on the upper face 106 times. Now the die is thrown at random. What is the probability of getting a 2 ?

(i)

52
275
(ii)

9
46
(iii)

53
275
(iv)

222
275
(v)

54
275

Question 21

21.

225 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

90

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

(i)

18
25
(ii)

7
25
(iii)

8
25
(iv)

6
25
(v)

4
13

Question 22

22.

Three coins are tossed simultaneously 235 times with the following frequencies of different outcomes :

Outcome

3 heads

2 heads

1 heads

No heads

Frequency

40

60

65

70

If the three coins are simultaneously tossed again, compute the probability of 'No heads' coming up.

(i)

5
16
(ii)

33
47
(iii)

15
47
(iv)

13
47
(v)

14
47

Question 23

23.

A die is thrown 300 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

25

30

45

60

65

75

If the die is thrown again randomly, find the probability of getting 6 as outcome.

(i)

1
2
(ii)

0
(iii)

1
4
(iv)

2
5
(v)

3
4

Question 24

24.

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

2

25

15

5

6

5

26

2

What is the empirical probability that an engineer lives less than 6 km from her place of work?

(i)

1
2
(ii)

2
3
(iii)

4
5
(iv)

3
4
(v)

5
6

Question 25

25.

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

20

11

3

4

26

16

12

21

7

12

30

4

4

29

21

What is the empirical probability that an engineer lives greater than 4 km from her place of work?

(i)

11
15
(ii)

2
3
(iii)

4
5
(iv)

3
4
(v)

4
15

Question 26

26.

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

(i)

1
365
(ii)

364
365
(iii)

365
366
(iv)

1
(v)

363
365

Question 27

27.

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

(i)

364
365
(ii)

0
(iii)

1
183
(iv)

1
365
(v)

2
365

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)

3
4
(v)

1
4

Question 29

29.

A carton consist of 84 shirts of which 68 are good, 11 have minor defects and 5 have major defects. Akhil, a trader, will only accept the shirts which are good, but Bhavani, 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 Akhil?

(i)

17
21
(ii)

4
21
(iii)

6
7
(iv)

9
11
(v)

16
21

Question 30

30.

A carton consist of 103 shirts of which 88 are good, 14 have minor defects and 1 have major defects. Gowtham, a trader, will only accept the shirts which are good, but Geetika, 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 Geetika?

(i)

101
103
(ii)

1
(iii)

103
104
(iv)

102
103
(v)

1
103

Question 31

31.

A lot of 30 bulbs contain 7 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective ?

(i)

4
15
(ii)

7
30
(iii)

23
30
(iv)

8
31
(v)

1
5

Question 32

32.

A lot of 34 bulbs contain 6 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)

9
11
(ii)

10
11
(iii)

5
6
(iv)

8
11
(v)

2
11

Question 33

33.

A box contains 30 discs which are numbered from 1 to 30. If one disc is drawn at random from the box, find the probability that it bears a two-digit number.

(i)

8
11
(ii)

4
5
(iii)

7
10
(iv)

3
5
(v)

3
10

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)

3
25
(ii)

43
50
(iii)

7
50
(iv)

8
51
(v)

4
25

Question 35

35.

A box contains 80 discs which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears a number divisible by 5.

(i)

1
3
(ii)

4
5
(iii)

1
5
(iv)

0
(v)

2
5

Question 36

36.

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

(i)

3
4
(ii)

1
4
(iii)

1
2
(iv)

4
5
(v)

1

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)

3
4
(v)

2
3

Question 38

38.

95 cards are numbered 1,2,3,....95 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)

71
95
(ii)

5
19
(iii)

25
96
(iv)

24
95
(v)

23
95

Question 39

39.

91 cards are numbered 1,2,3,....91 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)

19
91
(ii)

17
91
(iii)

19
92
(iv)

73
91
(v)

18
91

Question 40

40.

82 cards are numbered 1,2,3,....82 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 17?

(i)

8
41
(ii)

3
14
(iii)

7
41
(iv)

33
41
(v)

9
41

Question 41

41.

56 cards are numbered 1,2,3,....56 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 22?

(i)

4
7
(ii)

17
28
(iii)

11
28
(iv)

9
14
(v)

18
29

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 8.00 cm?

(i)

15
161
(ii)

17
162
(iii)

16
161
(iv)

17
161
(v)

145
161

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)

2
9
(ii)

7
8
(iii)

0
(iv)

1
8
(v)

1
4

Assignment Key