Exercise MCQ

Question 1

In a sample survey of 645 people, it was found that 516 people have a high school certificate. If a person is chosen at random, what is the probability that he/she has a high school certificate?

(a) 

(b) 

(c) 

(d) Solution 1

Correct option: (d)

Total number of people = 645

Number of people having high school certificate = 516

Question 2

In a medical examination of students of a class, the following blood groups are recorded:

Blood group	A	B	AB	O
Number of students	11	15	8	6

From this class, a student is chosen at random. What is the probability that the chosen student has blood group AB?

(a) 

(b) 

(c) 

(d) Solution 2

Correct option: (c)

Total number of students = 11 + 15 + 8 + 6 = 40

Number of students having blood group AB = 8 

Question 3

80 bulbs are selected at random from a lot and their lifetime in hours is recorded as under.

Lifetime (in hours)	300	500	700	900	1100
Frequency	10	12	23	25	10

One bulb is selected at random from the lot. What is the probability that its life is 1150 hours?

(a) 

(b) 

(c) 1

(d) 0Solution 3

Correct option: (d)

Total number of bulbs = 80

Number of bulbs having life of 1150 hours = 0

∴ Required probability = 0 Question 4

In a survey of 364 children aged 19 – 36 months, it was found that 91 liked to eat potato chips. If a child is selected at random, the probability that he/she does not like to eat potato chips is

(a) 

(b) 

(c) 

(d) Solution 4

Correct option: (c)

Total number of children = 364

Number of children who like to eat potato chips = 91

⇒ Number of children who do not like to eat potato chips = 364 – 91 = 273

Question 5

Two coins are tossed 1000 times and the outcomes are recorded as given below:

Number of heads	2	1	0
Frequency	200	550	250

Now, if two coins are tossed at random, what is the probability of getting at most one head?

(a) 

(b) 

(c) 

(d) Solution 5

Correct option: (b)

Total number of outcomes = 1000

Question 6

80 bulbs are selected at random from a lot and their lifetime in hours is recorded as under.

Lifetime (in hours)	300	500	700	900	1100
Frequency	10	12	23	25	10

One bulb is selected at random from the lot. What is the probability that selected bulb has a life more than 500 hours?

(a) 

(b) 

(c) 

(d) Solution 6

Correct option: (b)

Total number of bulbs = 80

Question 7

To know the opinion of the students about the subject Sanskrit, a survey of 200 students was conducted. The data is recorded as under.

Opinion	like	dislike
Number of students	135	65

What is the probability that a student chosen at random does not like it?

(a) 

(b) 

(c) 

(d) Solution 7

Correct option: (c)

Total number of students = 200

Number of students who does not like Sanskrit = 65

Question 8

A coin is tossed 60 times and the tail appears 35 times. What is the probability of getting a head?

Solution 8

Question 9

It is given that the probability of winning a game is 0.7. What is the probability of losing the game?

(a) 0.8

(b) 0.3

(c) 0.35

(d) 0.15Solution 9

Question 10

In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays. What is the probability that in given throw, the ball does not hit the boundary?

Solution 10

Question 11

A bag contains 16 cards bearing number 1, 2, 3,…, 16 respectively. One card is chosen at random. What is the probability that the chosen card bears a number which is divisible by 3?

Solution 11

Question 12

A bag contains 5 red, 8 black and 7 white balls. One ball is chosen at random. What is the probability that the chosen ball is black

Solution 12

Question 13

In 65 throws of a die, the outcomes were noted as under:

Outcomes	1	2	3	4	5	6
Number of times	8	10	12	16	9	10

A die is thrown at random. What is probability of getting a prime number

Solution 13

Question 14

In 50 throws of a die, the outcomes were notes as under:

Outcome	1	2	3	4	5	6
Number of times	8	9	6	7	12	8

A die is thrown at random. What is the probability of getting an even number?

Solution 14

Question 15

The table given below shows the month of birth of 36 students of a class :

Month of birth	Jan	Feb	March	April	May	June	July	Aug	Sept	Oct	Nov	Dec
No.of students	4	3	5	0	1	6	1	3	4	3	4	2

A student is chosen at random from the class. What is the probability that the chosen student was born in October?

Solution 15

Question 16

Two coins are tossed simultaneously 600 times to get

2 heads: 234 times, 1 head: 206 times, 0 head: 160 times.

If two coins are tossed at random, what is the probability of getting at least one head?

(a) 

(b) 

(c) 

(d) Solution 16

Correct option: (c)

Total number of outcomes = 600

Exercise Ex. 19

Question 1

_{A coin is tossed 500 times we get}

_{Head: 285 times, Tail: 215 times.}

_{When a coin is tossed at random, what is the probability of getting (i) A head? (ii) A tail?}Solution 1

Question 2

_{Two coin are tossed 400 times and we get}

_{two heads:112 times; one head :160 times; 0 head :128 times.}

_{When two coins are tossed at random, what is the probability of getting}

_{(i) 2 heads? (ii)1 head? (iii)0 head?}Solution 2

Question 3

Three coins are tossed 200 times and we get

three heads: 39 times; two heads: 58 times;

one head: 67 times; 0 head : 36 times.

When three coins are tossed at random, what is the probability of getting

(i) 3 heads? (ii) 1 head? (iii) 0 head? (iv) 2 heads?Solution 3

Question 4

A die is thrown 300 times and the outcomes are noted as given below:

Outcome	1	2	3	4	5	6
frequency	60	72	54	42	39	33

When a die is thrown at random, what is the probability of getting a

(i) 3? (ii) 6? (iii) 5? (iv)1?Solution 4

Question 5

In a survey of 200 ladies, it was found that 142 like coffee, while 58 dislike it.

Find the probability that a lady chosen at random

(i) Likes coffee (ii) dislikes coffeeSolution 5

Question 6

The percentages of marks obtained by a student in six unit tests are given below :

Unit test	I	II	III	IV	V	VI
Percentageof marksobtained	53	72	28	46	67	59

A unit test is selected at random. What is the probability that the student gets more than 60% marks in the test?Solution 6

Number of tests in which he gets more than60% marks =2

Total numbers of tests =6

_{Required probability}

Question 7

On a particular day, at a crossing in a city, the various types of 240 vehicles going past during a time interval were observed as under:

Type of vehicles	Two-wheelers	Three-wheelers	Four -wheelers
Frequency	84	68	88

Out of these vehicles, one is chosen at random. What is the probability that the chosen vehicle is a two-wheeler?Solution 7

Question 8

On one page of a telephone directory, there are 200 phone numbers. The frequency distribution of their units digits is given below:

Units digit	0	1	2	3	4	5	6	7	8	9
Frequency	19	22	23	19	21	24	23	18	16	15

One of the numbers is chosen at random from the page. What is the probability that the units digit of the chosen number is (i) 5? (ii) 8?Solution 8

Question 9

The following table shows the blood groups of 40 students of the class.

Blood Group	A	B	O	AB
Number of students	11	9	14	6

One student of the class is chosen at random. What is the probability that the chosn student has blood group

(i) O? (ii) AB?Solution 9

Question 10

12 packets of salt, each marked 2 kg, actually contained the following weights (in kg) of salt:

1.950, 2.020, 2.060, 1.980, 2.030, 1.970,

2.040, 1.990, 1.985, 2.025, 2.000, 1.980.

Out of these packets, one packet is chosen at random.

What is the probability that the chosen packet contains more than 2 kg of salt?Solution 10

Total number of salt packets = 12

Number of packets containing more than 2 kg of salt = 5

Therefore, 

Probability that the chosen packet contains more than 2 kg of salt

Question 11

In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays. Find the probability that he did not hit a boundary.Solution 11

Total number of ball played = 30

Number of times boundary was hit = 6

⇒ Number of times boundary was not hit = 30 – 6 = 24

Therefore, 

Probability that the batsman did not hit the boundary

Question 12

An organisation selected 2400 families at random and surveyed them to determine a relationship between the income level and the number of vehicles in a family. The information gathered is listed in the table below:

Monthly income (in Rs.)	Number of vehicles per family
0	1	2	3 or more
Less than Rs.25000	10	160	25	0
Rs.25000 – Rs.30000	0	305	27	2
Rs.30000 – Rs.35000	1	535	29	1
Rs.35000 – Rs.40000	2	469	59	25
Rs.40000 or more	1	579	82	88

Suppose a family is chosen at random. Find the probability that the family chosen is

(i) earning Rs.25000 – Rs.30000 per month and owning exactly 2 vehicles.

(ii) earning Rs.40000 or more per month and owning exactly 1 vehicle.

(iii) earning less than Rs.25000 per month and not owning any vehicle.

(iv) earning Rs.35000 – Rs.40000 per month and owning 2 or more vehicles.

(v) owning not more than 1 vehicle.Solution 12

Question 13

The table given below shows the mark obtained by 30 students in a test.

Marks(Class interval)	1 – 10	11 – 20	21 – 30	31 – 40	41 – 50
Number of students(Frequency)	7	10	6	4	3

Out of these students, one is chosen at random. What is the probability that the marks of the chosen student

(i) are 30 or less?

(ii) are 31 or more?

(iii) lie in the interval 21-30?Solution 13

Question 14

The table given shows the ages of 75 teachers in a school.

Age (in years)	18 – 29	30 – 39	40 – 49	50 – 59
Number of teachers	3	27	37	8

A teacher from this school is chosen at random. What is probability that the selected teacher is

(i) 40 or more than 40 years old?

(ii) of an age lying between 30-39 years (including both)?

(iii) 18 years or more and 49 years or less?

(iv) 18 years or more old?

(v) above 60 years of age?

NOTE Here 18 – 29 means 18 or more but less than or equal to 29.Solution 14

Question 15

Following are the ages (in years) of 360 patients, getting medical treatment in a hospital:

Age(in years)	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70
Number of patients	90	50	60	80	50	30

One of the patients is selected at random.

What is probability that his age is

(i) 30 years or more but less than 40 years?

(ii) 50 years or more but less than 70 years?

(iii) 10 years or more but less than 40 years?

(iv) 10 years or more?

(v) less than 10 years?Solution 15

Question 16

The marks obtained by 90 students of a school in mathematics out of 100 are given as under:

Marks	0-20	20-30	30-40	40-50	50-60	60-70	70 and above
No. of students	7	8	12	25	19	10	9

From these students, a student is chosen at random.

What is the probability that the chosen student

(i) get 20% or less marks? (ii) get 60% or more marks?Solution 16

Question 17

It is known that a box of 800 electric bulbs contains 36 defective bulbs. One bulb is taken at random out of the box. What is probability that the bulb chosen is nondefective?Solution 17

Total number of electric bulbs = 800

Number of defective bulbs = 36

⇒ Number of non-defective bulbs = 800 – 36 = 764

Hence, probability that the bulb chosen is non-defective

Question 18

Fill in the blanks.

(i) Probability of an impossible event = ….. .

(ii) Probability of a sure event = ….. .

(iii) Let E be an event. Then, P(not E) = ….. .

(iv) P(E) + P(not E) = ….. .

(v) ….. ≤ P(E) ≤ …. .Solution 18

Fill in the blanks.

(i) Probability of an impossible event = 0

(ii) Probability of a sure event = 1

(iii) Let E be an event. Then, P(not E) = 1 – P(E)

(iv) P(E) + P(not E) = 1

(v) 0 ≤ P(E) ≤ 1