EduSahara™ Worksheet

Question 1

1.

On a particular day, at a crossing in a city, the various types of 110 vehicles going past during a time-interval were observed as under:

Type of Vehicle

Four-wheeler

Two-wheeler

Three-wheeler

Frequency

25

40

45

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

(i)

7
11
(ii)

3
11
(iii)

5
11
(iv)

4
11
(v)

5
12

Question 2

2.

The following table shows the blood-groups of 297 students of a class.

Blood group

O

AB

A

B

Number of students

45

54

63

135

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

(i)

6
11
(ii)

5
11
(iii)

1
2
(iv)

4
11

Question 3

3.

A bag contains 20 blue balls, 65 black balls, 30 yellow balls and 75 gray balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is gray.

(i)

23
38
(ii)

16
39
(iii)

7
19
(iv)

8
19
(v)

15
38

Question 4

4.

A box contains 12 red balls, 18 orange balls, 27 gray balls and 33 blue balls. One ball is drawn at random from the box. Find the probability that the ball drawn is not blue.

(i)

3
5
(ii)

11
30
(iii)

19
30
(iv)

2
3
(v)

20
31

Question 5

5.

A box contains 10 blue balls, 12 orange balls, 22 white balls and 24 black balls. One ball is drawn at random from the box. Find the probability that the ball drawn is orange or white.

(i)

3
4
(ii)

1
2
(iii)

5
6
(iv)

4
5
(v)

2
3

Question 6

6.

A box contains 24 gray marbles, 21 black marbles, 6 red marbles and 18 white marbles. One marble is drawn at random from the box. Find the probability that the marble drawn is neither gray nor black.

(i)

9
23
(ii)

7
23
(iii)

15
23
(iv)

8
23
(v)

3
8

Question 7

7.

What is the probability of a sure event?

(i)

1
4
(ii)

1
2
(iii)

3
4
(iv)

1
(v)

0

Question 8

8.

What is the probability of an impossible event?

(i)

1
(ii)

1
4
(iii)

0
(iv)

3
4
(v)

1
2

Question 9

9.

There are 50 students in a class room of whom 26 are boys and 24 are girls. From these students, one is choosen at random. What is the probability that the choosen student is a boy ?

(i)

13
25
(ii)

7
13
(iii)

14
25
(iv)

12
25

Question 10

10.

There are 52 students in a class room of whom 26 are boys and 26 are girls. From these students, one is choosen at random. What is the probability that the choosen student is a girl ?

(i)

3
4
(ii)

4
5
(iii)

2
3
(iv)

5
6
(v)

1
2

Question 11

11.

In a lottery, there are 18 prizes and 15 blanks. What is the probability of getting a prize?

(i)

7
11
(ii)

7
12
(iii)

5
11
(iv)

6
11

Question 12

12.

In a lottery, there are 20 prizes and 18 blanks. What is the probability of not getting a prize?

(i)

1
2
(ii)

9
19
(iii)

10
19
(iv)

8
19

Question 13

13.

Which of the following are true?

a)	Probability of getting 109 marks out of 100 is 1.09
b)	The probability of an event that cannot happen is unknown
c)	If the probability is too less, it will become negative
d)	The probability of an event that is very likely to happen is 1
e)	If the probability of failing the exam is 0.5, the probability of passing the exam is 0.5

(i)

{c,d,e}
(ii)

{a,e}
(iii)

{b,e}
(iv)

{e}

Question 14

14.

Which of the following experiments have equally likely outcomes?

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

(i)

{b,e,d}
(ii)

{d,e}
(iii)

{c,a,d}
(iv)

{b,e}
(v)

{a,d}

Question 15

15.

Which of the following are possible values of probability?

a)

5

b)

6

7

c)

-5.3

d)

0.33

e)

7

1

(i)

{e,a,b}
(ii)

{a,b}
(iii)

{c,d,b}
(iv)

{c,d}
(v)

{b,d}

Question 16

16.

If P(E) =
0.25
, find P(
E
)

(i)

1.75
(ii)

0.75
(iii)

2.75
(iv)

7.75
(v)

8.75

Question 17

17.

Which of the following are true?

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

(i)

{e,a,b}
(ii)

{d,c,b}
(iii)

{a,b}
(iv)

{b,c}
(v)

{d,c}

Question 18

18.

Which of the following are true?

a)

P(E) - P(
E
) = 0

b)

P(E) + P(
E
) = 0

c)

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

d)

P(E) = 1 - P(
E
)

e)

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

(i)

{e,a,c}
(ii)

{b,d,c}
(iii)

{b,d}
(iv)

{c,d}
(v)

{a,c}

Question 19

19.

Two players Priyanka and Anjali play a tennis match. It is known that the probability of Priyanka winning the match is 0.75. What is the probability of Anjali winning the match?

(i)

3
4
(ii)

0
(iii)

1
2
(iv)

1
4
(v)

2
5

Question 20

20.

A die is thrown 600 times. The number 5 appears on the upper face 94 times. Now the die is thrown at random. What is the probability of getting a 5 ?

(i)

253
300
(ii)

23
150
(iii)

4
25
(iv)

48
301
(v)

47
300

Question 21

21.

351 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

99

108

144

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

(i)

11
39
(ii)

10
39
(iii)

3
10
(iv)

4
13
(v)

28
39

Question 22

22.

Three coins are tossed simultaneously 190 times with the following frequencies of different outcomes :

Outcome

3 heads

2 heads

1 heads

No heads

Frequency

30

45

50

65

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

(i)

14
39
(ii)

7
19
(iii)

25
38
(iv)

6
19
(v)

13
38

Question 23

23.

A die is thrown 460 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

40

55

80

85

95

105

If the die is thrown again randomly, find the probability of getting 2 as outcome.

(i)

3
23
(ii)

4
31
(iii)

11
92
(iv)

5
46
(v)

81
92

Question 24

24.

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

11

10

14

30

29

21

26

30

17

11

5

8

18

What is the empirical probability that an engineer lives less than 26 km from her place of work?

(i)

10
13
(ii)

8
13
(iii)

5
7
(iv)

4
13
(v)

9
13

Question 25

25.

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

3

24

6

19

20

25

26

11

5

24

9

14

24

16

16

What is the empirical probability that an engineer lives greater than 19 km from her place of work?

(i)

1
2
(ii)

1
5
(iii)

3
5
(iv)

2
5

Question 26

26.

Savitha and Manisha 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)

363
365
(v)

1

Question 27

27.

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

(i)

0
(ii)

1
183
(iii)

364
365
(iv)

2
365
(v)

1
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)

0
(iii)

1
4
(iv)

1
2
(v)

3
4

Question 29

29.

A carton consist of 98 shirts of which 78 are good, 15 have minor defects and 5 have major defects. Mahender, a trader, will only accept the shirts which are good, but Akshaya, 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 Mahender?

(i)

40
49
(ii)

38
49
(iii)

4
5
(iv)

39
49
(v)

10
49

Question 30

30.

A carton consist of 64 shirts of which 55 are good, 6 have minor defects and 3 have major defects. Bali, 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)

3
64
(ii)

61
64
(iii)

31
32
(iv)

62
65
(v)

15
16

Question 31

31.

A lot of 20 bulbs contain 8 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective ?

(i)

3
5
(ii)

2
5
(iii)

1
5
(iv)

1
2

Question 32

32.

A lot of 38 bulbs contain 13 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)

25
37
(ii)

13
37
(iii)

23
37
(iv)

25
38
(v)

24
37

Question 33

33.

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 two-digit number.

(i)

4
5
(ii)

21
25
(iii)

9
50
(iv)

14
17
(v)

41
50

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)

43
50
(ii)

8
51
(iii)

4
25
(iv)

7
50
(v)

3
25

Question 35

35.

A box contains 60 discs which are numbered from 1 to 60. 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)

0
(iv)

1
5
(v)

2
5

Question 36

36.

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

(i)

4
5
(ii)

1
2
(iii)

1
4
(iv)

1
(v)

3
4

Question 37

37.

84 cards are numbered 1,2,3,....84 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)

4
5
(ii)

1
2
(iii)

2
3
(iv)

3
4
(v)

5
6

Question 38

38.

77 cards are numbered 1,2,3,....77 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)

1
3
(ii)

3
11
(iii)

8
11
(iv)

2
11
(v)

4
11

Question 39

39.

98 cards are numbered 1,2,3,....98 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)

79
98
(ii)

20
99
(iii)

10
49
(iv)

19
98
(v)

9
49

Question 40

40.

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 less then 25?

(i)

4
11
(ii)

8
11
(iii)

3
11
(iv)

2
11
(v)

1
3

Question 41

41.

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 greater then 25?

(i)

58
83
(ii)

57
82
(iii)

25
82
(iv)

29
41
(v)

28
41

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 6.00 cm?

(i)

1
7
(ii)

6
7
(iii)

2
7
(iv)

0
(v)

1
4

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)

1
4
(iii)

0
(iv)

1
8
(v)

7
8

Assignment Key