From chapter Probability, Some of the important questions are covered in this question paper. Questions that covers from the creative as well as previous year questions.

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Questions:

Generic 3

5 x 3 = 15

In a one-day cricket Match, Sachin palyed 40 balls and hit 12 sixes and Saurav played 30 balls and hit 9 fours. Find the probability that Sachin will hit a six in the next ball and also find the probability that Saurav will not hit a four in the next ball.

Marks obtained by 90 students in a particular subject out of a total of 100 are given below, find the probability that a student selected obtained marks 60 or above and a student selected obtained less than 40.

Marks out of 100	No. of students
0-20	7
20-30	10
30-40	10
40-50	20
50-60	20
60-70	15
70 and above	8

The data regarding the number of children in a house of a colony which has 250 houses was collected and is recorded below. The houses with number of children are recorded below:

No.of children	No.of houses
1 child	48
2 boys	72
2 girls	63
1 boy and 1 girl	55
No child	12

One house is selected at random. What is the probability that it is a house which has
(a) 2 boys?
(b) more than one child?
(c) no children at all?

The weekly pocket expenses of students are given below. Find the probability that the weekly pocket expenses of a student are:
(i) Rs 59
(ii) more than Rs 59
(iii) less than Rs 59

Pocket expenses (in Rs)	No.of students
45	7
40	4
59	10
71	6
58	3
63	8
65	1

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

Outcome	3 heads	2 heads	1 head	No head
Frequency	23	72	77	28

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

Multiple Choice Question

10 x 1 = 10

The probability of guessing the correct answer to a certain question is \(\frac { x }{ 2 } \) . If the probability of not guessing the correct answer to the question is \(\frac { 2 }{ 3 } \) , then x=..............

(a)

\(\frac { 4 }{ 3 } \)

(b)

\(\frac { 3 }{ 4 } \)

(c)

\(\frac { 2 }{ 3 } \)

(d)

\(\frac { 1 }{ 3 } \)

11 bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg) 4.97,5.05,5.08,5.03,5.00,5.06, 4.98, 5.04, 5.08, 5.07, 5.00. The probability that a bag chosen at random, contains more than 5 kg of flour is:

(a)

\(\frac { 2 }{ 11 } \)

(b)

\(\frac { 4 }{ 11 } \)

(c)

\(\frac { 9 }{ 11 } \)

(d)

\(\frac { 7 }{ 11 } \)

Ten cards numbered 1,2, ... , 10 are put in a box. If a card is drawn at random, then the probability that the card drawn is a prime number is:

(a)

\(\frac { 7 }{ 10 } \)

(b)

\(\frac { 3 }{ 5 } \)

(c)

\(\frac { 2 }{ 5 } \)

(d)

\(\frac { 1 }{ 2 } \)

Two coins are tossed simultaneously 1000 times and we get
Two heads: 200 times
One head: 600 times
No head: 200 times
Find the probability of getting 1 head is

(a)

\(\frac { 1 }{ 5 } \)

(b)

\(\frac { 2 }{ 5 } \)

(c)

\(\frac { 3 }{ 5 } \)

(d)

\(\frac { 4 }{ 5 } \)

10.

In a cricket match, a batsman hits a boundary on 4 balls that he faced. If he did not hit a boundary on the remaining 20 balls that he faced, then the probability of hitting boundary is:

(a)

\(\frac { 1 }{ 5 } \)

(b)

\(\frac { 4 }{ 5 } \)

(c)

\(\frac { 1 }{ 6 } \)

(d)

\(\frac { 5 }{ 6 } \)

11.

Reena dialed a phone number 100 times in a week out of which she gets the response 55 times.The probability that she will not get the response is:

(a)

\(\frac { 55 }{ 100 } \)

(b)

\(\frac { 100 }{ 55 } \)

(c)

\(\frac { 45 }{ 100 } \)

(d)

\(\frac { 100 }{ 45 } \)

12.

A coin is tossed 100 times with the following frequencies:
Head :75, Tai l: 25
Find the probability of getting a head.

(a)

\(\frac { 1 }{ 4 } \)

(b)

\(\frac { 1 }{ 2 } \)

(c)

\(\frac { 3 }{ 4 } \)

(d)

13.

In an experiment, E and F are the only two possible outcomes.If P(E)=0.72, then P(F) is equal to

(a)

0.38

(b)

0.28

(c)

0.72

(d)

any value between 0 and 1

14.

What is the number of outcomes when a coin is tossed?

(a)

(b)

(c)

(d)

15.

The minimum probability of an event is

(a)

(b)

(c)

\(\frac { 1 }{ 2 } \)

(d)

-1

Generic 4

5 x 4 = 20

16.

Mr. Kakkad's son Cheeku is sufering from a disease for 20 days and is hospitalised. Doctor asks Mr.Kakkad to donate blood in order to fulfill Cheeku's need. A pathologist tests and tells Mr.Kakkad, "Your blood group cannot be given to your son." After this Mr.Kakkad thinks of an idea and uploads a request of blood requirement on Facebook as soon as possible. In a short time, 85 blood of only three of them may be used for Cheeku.
(i) What is the probability that the blood group of a person chosen at random out of the donors cannot be given to Cheeku?
(ii) Which value is depicted by Mr.Kakkad regarding his son?
(iii) Which value (s) is (are) depicted by 85 blood donors?

17.

The percentage of marks obtained by a student in monthly unit test are given below:

Test	I	II	III	IV	V	VI
Percentage of Marks	52	60	65	75	80	72

Find the probability that in the next test the students sets
(i) more than 70% marks
(ii) less than 70% marks
(iii) at least 60 marks

18.

An insurance company selected 1600 drivers at random in a particular city to find a relationship between age and number of accidents. The data obtained are given in the following table:

Age of drivers (in years)	No.of accidents(in one year)
Age of drivers (in years)	0	1	2	3	More than 3
18-25	320	125	75	45	30
25-40	400	45	50	15	10
40-55	150	85	13	8	10
Above 55	150	25	17	20	7

Find the number of drivers
(a) in the age of 25-40 years and has more than 2 accidents in the year.
(b) in the age above 40 years and has accidents more than 1 but less than 3.

19.

On a particular day, the number of vehicles through a crossing is given below:

Vehicle	Frequency
Two-wheeler	57
Three-wheeler	33
Four-wheeler	30

A particular vehicle is chosen at random. What is the probability that it is not a four-wheeler?

20.

1500 families with 2 children were released randomly and the following data was recorded:

No.of girls	No.of.families
0	211
1	814
2	475

If a family is chosen at random, find the probability that it has
(i) at most one girl
(ii) at least one girl

Generic 2

5 x 2 = 10

21.

There are 13 girls and 15 boys in a line. If one student is chosen at random, then find the probability that he is a boy.

22.

On a particular day, the number of vehicles passing through a crossing is given below:

Vehicle	2 wheeler	3 wheeler	4 wheeler
Frequency	57	33	30

A particular vehicle is chosen at random. What is the probability that it is not a four wheeler?

23.

A bag contains 190 coins out of which, fifty Rs 2 coins, forty Rs 1 coins and rest Rs 5 coins. One coin is selected at random. Find the probability that it is a Rs 5 coin.

24.

A bag has 3 red and 7 black balls. One ball is taken out of the bag. Find the probability that it is a
(i) red ball
(ii) blackball.

25.

A die was rolled 100 times and the number of times 6 came up was noted. If the experimental probability calculated from this information is \(\frac { 2 }{ 5 } \)then how many times 6 came up? Justify your answer.

1 Marks

1 x 1 = 1

26.

A die is thrown, what will be the probability of getting an even number?

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Answers Key:

Generic 3

5 x 3 = 15

Total number of balls faced by Sachin = 40
No. of balls on which he hit a six = 12
Let E₁, be the event of hitting a six.
\(\therefore \)No. of outcomes = 12
\(\therefore P(E_1)=\frac{12}{40}=\frac{3}{10}\)
Now, total No. of balls faced by Saurav = 30
Let E₂ be the event of Saurav did not hit the boundary
No. of outcomes = 30 - 9 = 21
\(P(E_2)=\frac{21}{30}=\frac{7}{10}\)

Number of students obtained marks 60 or above =15+8=23
\(\therefore \)P(marks 60 or above)\(=\frac{23}{90}\)
Students who obtained marks less than 40=7+10+10=27
P(marks less than 40)\(=\frac{27}{90}\)

\((a)\frac { 36 }{ 125 } \)
\((b)\frac { 19 }{ 25 } \)
\((c)\frac { 6 }{ 125 } \)

\((i)\frac { 10 }{ 39 }\)
\((ii)\frac { 5 }{ 13 }\)
\((iii)\frac { 14 }{ 39 } \)

Total number of times the three coins are tossed = 200
Number of times when 2 heads come up = 72
Probability of 2 heads coming up
=\(\frac { 72 }{ 200 } =\frac { 9 }{ 25 } \)

Multiple Choice Question

10 x 1 = 10

\(\frac { x }{ 2 } +\frac { 2 }{ 3 } =1\)

(d)
\(\frac { 7 }{ 11 } \)

Required probability=\(\frac { 600 }{ 1000 } =\frac { 3 }{ 5 } \)

10.

Required probability=4/4+20

11.

Required probability=\(\frac { 100-55 }{ 100 } =\frac { 45 }{ 100 } \)

12.

13.

P(E)+P(F)=1

14.

H,T

15.

\(0\le P(E)\le 1\)

Generic 4

5 x 4 = 20

16.

Total number blood donors = 85
(i) Number of donors whose blood is useful for Cheeku = 3
\(\therefore \) Number of favourable events = 85 - 3 = 82
Now, required probability\(=\frac{82}{85}\)
(ii) Responsible, rationality, love
(iii) Blood donation helps the needy. In fact it is a great act of charity and co-operation.

17.

(i) Number of test in which the student scored more than 70%marks=3
P(more than 70%marks)\(=\frac{3}{6}=\frac{1}{2}\)
(ii) Number of test in which the students scored less than 70% marks =3
P(more than 70% marks)\(=\frac{3}{6}=\frac{1}{2}\)
(iii) Number of tests in which the students scored at lear 60% marks=5
P(at least 60% marks) = \(\frac{5}{6}\)

18.

(a) The number of drivers in the age of 25-40 years and has more than 2 accidents in the year
= 15 + 10 = 25
(b) The number of drivers the age of whose is above 40 years and has accidents more than 1 but less than 3
= 13 + 17 = 30.

19.

Number of two wheelers = 57
Number of three wheelers = 33
Number of four wheelers = 30
Total number of vehicles = 57 + 33 + 30 = 120
Number of vehicles that is not a four-wheeler = 57 + 33 = 90
Probability that the vehicle chosen at random is not a four-wheeler
\(\frac { 90 }{ 120 } =\frac { 3 }{ 4 } \)

20.

Total number of families = 1500
(i) at most one girl means 0 girl or 1 girl.
Number of families which have at most one girl
= Number of families which have 0 girl + Number of families which have 1 girl.
= 211 + 814 = 1015
Probability that it has at most one girl=\(\frac { 1015 }{ 1500 } =\frac { 203 }{ 300 } \)
(ii) at least one girl means 1 girls or 2 girls.
Number of families which have at least one girl
= Number of families which have I girl + Number of families which have 2 girls.
= 814 + 475 = 1289
Probability that it has at least one girl=\(\frac { 1289 }{ 1500 } \)

Generic 2

5 x 2 = 10

21.

Number of Boys = 15
NUmber of Girls = 13
\(\therefore \)Total Number of Student = 15 +13 = 28
Probability of selecting a boy\(=\frac{15}{28}\)

22.

Total number of vehicles = 57 + 33 + 30 = 120
Vehicles which are not four wheelers = 57 + 33 = 90
\(\therefore \)P(chosen vehicle is not four wheeler)\(=\frac{90}{120}=\frac{3}{4}\)

23.

\(\frac { 10 }{ 19 } \)

24.

\((i)\frac { 3 }{ 10 }\)
\((ii)\frac { 7 }{ 10 } \)

25.

1 Marks

1 x 1 = 1

26.