EduSahara™ Worksheet

Question 1

1.

On a particular day, at a crossing in a city, the various types of 140 vehicles going past during a time-interval were observed as under:

Type of Vehicle

Four-wheeler

Three-wheeler

Two-wheeler

Frequency

30

45

65

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

(i)

2
7
(ii)

9
28
(iii)

5
14
(iv)

19
28
(v)

10
29

Question 2

2.

The following table shows the blood-groups of 414 students of a class.

Blood group

AB

A

B

O

Number of students

45

108

117

144

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

(i)

41
46
(ii)

5
46
(iii)

6
47
(iv)

3
23
(v)

2
23

Question 3

3.

A box contains 48 red balls, 56 pink balls, 4 yellow balls and 32 gray balls. One ball is drawn at random from the box. Find the probability that the ball drawn is gray.

(i)

9
35
(ii)

8
35
(iii)

1
4
(iv)

27
35
(v)

1
5

Question 4

4.

A bag contains 9 pink balls, 21 yellow balls, 27 red balls and 39 black balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is not red.

(i)

9
32
(ii)

8
11
(iii)

3
4
(iv)

23
32
(v)

11
16

Question 5

5.

A bag contains 10 orange balls, 40 pink balls, 65 black balls and 10 red balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is orange or black.

(i)

3
5
(ii)

2
3
(iii)

4
5
(iv)

2
5

Question 6

6.

A box contains 56 white marbles, 8 black marbles, 60 gray marbles and 56 yellow marbles. One marble is drawn at random from the box. Find the probability that the marble drawn is neither gray nor white.

(i)

1
3
(ii)

29
45
(iii)

17
45
(iv)

16
45
(v)

17
46

Question 7

7.

What is the probability of a sure event?

(i)

1
4
(ii)

1
(iii)

3
4
(iv)

1
2
(v)

0

Question 8

8.

What is the probability of an impossible event?

(i)

1
2
(ii)

1
(iii)

3
4
(iv)

1
4
(v)

0

Question 9

9.

There are 72 students in a class room of whom 40 are boys and 32 are girls. From these students, one is choosen at random. What is the probability that the choosen student is a boy ?

(i)

3
5
(ii)

2
3
(iii)

5
9
(iv)

4
9

Question 10

10.

There are 56 students in a class room of whom 34 are boys and 22 are girls. From these students, one is choosen at random. What is the probability that the choosen student is a girl ?

(i)

11
28
(ii)

12
29
(iii)

3
7
(iv)

5
14
(v)

17
28

Question 11

11.

In a lottery, there are 23 prizes and 12 blanks. What is the probability of getting a prize?

(i)

22
35
(ii)

23
35
(iii)

2
3
(iv)

24
35
(v)

12
35

Question 12

12.

In a lottery, there are 19 prizes and 17 blanks. What is the probability of not getting a prize?

(i)

19
36
(ii)

1
2
(iii)

4
9
(iv)

17
36
(v)

18
37

Question 13

13.

Which of the following are true?

a)	The probability of an event that is very likely to happen is 1
b)	The probability of an event that cannot happen is unknown
c)	If the probability of failing the exam is 0.33, the probability of passing the exam is 0.67
d)	If the probability is too less, it will become negative
e)	Probability of getting 102 marks out of 100 is 1.02

(i)

{d,e,c}
(ii)

{b,c}
(iii)

{c}
(iv)

{a,c}

Question 14

14.

Which of the following experiments have equally likely outcomes?

a)	A true/false question is attempted. The answer is either right or wrong
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 baby is born. It is a boy or girl
e)	A man starts his vehicle. It starts or it does not starts

(i)

{c,d,a}
(ii)

{e,b,a}
(iii)

{b,a}
(iv)

{a,d}
(v)

{c,d}

Question 15

15.

Which of the following are possible values of probability?

a)

7

8

b)

0.25

c)

9

8

d)

-5.3

e)

2

(i)

{e,c,a}
(ii)

{c,a}
(iii)

{a,b}
(iv)

{d,b,a}
(v)

{d,b}

Question 16

16.

If P(E) =
0.43
, find P(
E
)

(i)

8.57
(ii)

7.57
(iii)

1.57
(iv)

2.57
(v)

0.57

Question 17

17.

Which of the following are true?

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

(i)

{a,d}
(ii)

{b,a}
(iii)

{c,d,a}
(iv)

{e,b,a}
(v)

{c,d}

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(
E
) = 0

d)

P(E) = 1 - P(
E
)

e)

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

(i)

{e,b,a}
(ii)

{a,d}
(iii)

{b,a}
(iv)

{c,d}
(v)

{c,d,a}

Question 19

19.

Two players Reshma and Kajal play a tennis match. It is known that the probability of Reshma winning the match is 0.67. What is the probability of Kajal winning the match?

(i)

8
25
(ii)

34
101
(iii)

33
100
(iv)

67
100
(v)

17
50

Question 20

20.

A die is thrown 330 times. The number 5 appears on the upper face 66 times. Now the die is thrown at random. What is the probability of getting a 5 ?

(i)

1
5
(ii)

1
3
(iii)

4
5
(iv)

2
5
(v)

0

Question 21

21.

288 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

90

135

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

(i)

1
4
(ii)

25
32
(iii)

7
32
(iv)

8
33
(v)

3
16

Question 22

22.

Three coins are tossed simultaneously 210 times with the following frequencies of different outcomes :

Outcome

3 heads

2 heads

1 heads

No heads

Frequency

35

40

65

70

If the three coins are simultaneously tossed again, compute the probability of '1 heads' coming up.

(i)

2
7
(ii)

29
42
(iii)

13
42
(iv)

14
43
(v)

1
3

Question 23

23.

A die is thrown 325 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

30

45

55

60

65

70

If the die is thrown again randomly, find the probability of getting 3 as outcome.

(i)

12
65
(ii)

2
13
(iii)

54
65
(iv)

11
65
(v)

2
11

Question 24

24.

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

14

19

5

14

26

5

27

25

3

15

8

11

26

What is the empirical probability that an engineer lives less than 27 km from her place of work?

(i)

11
13
(ii)

1
(iii)

1
13
(iv)

13
14
(v)

12
13

Question 25

25.

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

23

16

4

15

15

30

26

7

21

11

What is the empirical probability that an engineer lives greater than 30 km from her place of work?

(i)

3
4
(ii)

1
2
(iii)

1
4
(iv)

1
(v)

0

Question 26

26.

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

(i)

365
366
(ii)

364
365
(iii)

1
(iv)

363
365
(v)

1
365

Question 27

27.

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

(i)

1
365
(ii)

2
365
(iii)

0
(iv)

364
365
(v)

1
183

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)

1
4
(ii)

0
(iii)

1
2
(iv)

3
4
(v)

2
5

Question 29

29.

A carton consist of 64 shirts of which 51 are good, 11 have minor defects and 2 have major defects. Satya, a trader, will only accept the shirts which are good, but Kamala, 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 Satya?

(i)

25
32
(ii)

4
5
(iii)

51
64
(iv)

13
64
(v)

13
16

Question 30

30.

A carton consist of 86 shirts of which 74 are good, 10 have minor defects and 2 have major defects. Kumar, a trader, will only accept the shirts which are good, but Teena, 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 Teena?

(i)

42
43
(ii)

1
(iii)

43
44
(iv)

1
43
(v)

41
43

Question 31

31.

A lot of 23 bulbs contain 8 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective ?

(i)

7
23
(ii)

9
23
(iii)

15
23
(iv)

3
8
(v)

8
23

Question 32

32.

A lot of 35 bulbs contain 7 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)

13
17
(ii)

27
34
(iii)

4
5
(iv)

7
34
(v)

14
17

Question 33

33.

A box contains 20 discs which are numbered from 1 to 20. If one disc is drawn at random from the box, find the probability that it bears a two-digit number.

(i)

4
7
(ii)

9
20
(iii)

1
2
(iv)

3
5
(v)

11
20

Question 34

34.

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 perfect square number.

(i)

5
36
(ii)

3
35
(iii)

31
35
(iv)

4
35
(v)

1
7

Question 35

35.

A box contains 20 discs which are numbered from 1 to 20. If one disc is drawn at random from the box, find the probability that it bears a number divisible by 5.

(i)

0
(ii)

2
5
(iii)

4
5
(iv)

1
5
(v)

1
3

Question 36

36.

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

(i)

1
4
(ii)

3
4
(iii)

1
2
(iv)

1
(v)

4
5

Question 37

37.

81 cards are numbered 1,2,3,....81 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)

41
81
(ii)

14
27
(iii)

21
41
(iv)

40
81

Question 38

38.

93 cards are numbered 1,2,3,....93 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)

9
32
(ii)

7
31
(iii)

8
31
(iv)

23
31
(v)

9
31

Question 39

39.

69 cards are numbered 1,2,3,....69 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)

56
69
(ii)

4
23
(iii)

1
5
(iv)

13
69
(v)

14
69

Question 40

40.

74 cards are numbered 1,2,3,....74 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 21?

(i)

10
37
(ii)

9
37
(iii)

11
37
(iv)

27
37
(v)

11
38

Question 41

41.

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 greater then 24?

(i)

7
10
(ii)

24
79
(iii)

55
79
(iv)

54
79
(v)

56
79

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 20.00 cm?

(i)

67
231
(ii)

200
693
(iii)

199
693
(iv)

201
694
(v)

493
693

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)

1
16
(ii)

1
8
(iii)

0
(iv)

2
17
(v)

15
16

Assignment Key