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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?
The percentages of marks obtained by a student in six unit tests are given below:
Unit test | I | II | III | IV | V | VI |
Percentage of mark obtained | 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 ?
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 vehicle | 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?
On one page of a telephone directory, there are 200 phone number. 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 number is chosen at random from the page. What is the probability that the units digit of the chosen number is (i) 5? (8)?
The following table shows the blood groups of 40 students of a 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 chosen student has blood group(i) O? (ii) AB?
The table given below shows the marks obtained by 30 students in a test.
Marks (class interval) | Number of students (frequency) |
1-10 | 7 |
11-20 | 10 |
21-30 | 6 |
31-40 | 4 |
40-50 | 3 |
Out of these students, one is chosen at random. What is the probability that his marks lie in the interval 21-30?
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.
Find the probability that his age is
(i) 30 Year or more but less than 40 years.
(ii) 50 year or more but less than 70 years
(iii) Less than 10 years.
(iv) 10 years or more.
A survey of 200 persons of a locality shows the liking and disliking of tea.
No of persons who like tea | 148 |
No of persons who dislike tea | 52 |
Out of these one was chosen at random. What is the probability that the chosen person likes tea?
In a locality, 1000 families were chosen at random and the following data was collected:
Number of children in each family | 0 | 1 | 2 | 3 | 4 or more |
Number of families | 6 | 184 | 672 | 127 | 11 |
Out of these families, a family was chosen at random. What is the probability that the chosen family has 2 children?
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. | Sep. | Oct. | Nov. | Dec. |
No. of students | 4 | 3 | 5 | 0 | 1 | 6 | 1 | 3 | 4 | 3 | 4 | 2 |
A students is chosen at random from the class. What is the probability that the chosen student was born in October?
A die is thrown 40 times and each time the number on the uppermost face is noted. It was recorded as under:
Outcome | 1 | 2 | 3 | 4 | 5 | 6 |
Number of times | 5 | 6 | 8 | 10 | 7 | 6 |
A die is thrown at random, What is the probability of getting a 5?
In 50 throws of a die, the outcomes were noted as under:
Outcome | 1 | 2 | 3 | 4 | 5 | 6 |
Number of times | 8 | 9 | 6 | 7 | 12 | 8 |
A die is the at random. What is the probability of getting an even number?
In 65 thrown of a die, the outcomes were noted as under:
Outcome | 1 | 2 | 3 | 4 | 5 | 6 |
Number of times | 8 | 10 | 12 | 16 | 9 | 10 |
A die is thrown at random. What is the probability of getting a prime number?
On one page of a directory, there are 160 telephone numbers. The frequency distribution of the unit place digit is given as under:
Units place digit | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Frequency | 19 | 16 | 18 | 21 | 14 | 11 | 15 | 16 | 13 | 17 |
From this page, one of the numbers is chosen at random. What is the probability that the unit place digit in the chosen number is 6?
Two coins are tossed 1000 times and the outcomes are recorded as under:
Number of heads | 2 | 1 | 0 |
Frequency | 266 | 540 | 194 |
A coin is thrown at random. What is the probability of getting at most one head?
80 bulbs are selected at random from a lot and their lifetime is recorded in the from of a frequency table given below:
Lifetimes(in hours) | 300 | 500 | 700 | 900 | 1100 |
Frequency | 10 | 15 | 23 | 25 | 7 |
A bulb is chosen at random from the lot. What is the probability that the bulb chosen has lifetime less than 900 hours?
In a medical examination of 40 students of a class, the following blood, groups are recorded:
Blood group | A | B | AB | O |
No of students | 11 | 15 | 9 | 5 |
From this class, a student is chosen at random, What is the probability that the chosen student has blood group B?
A die is thrown 50 times and the outcomes are recorded as under.
Outcome | 1 | 2 | 3 | 4 | 5 | 6 |
No of times | 11 | 9 | 8 | 5 | 7 | 10 |
If a die is thrown at random, what is the probability of getting 8?
Each question consists of two statements, namely, Assertion(A) and Reason (R). Choose the correct options.
Assertion (A) | Reason (R) |
In a cricket match a batsman hits a boundary 9 times out of 45 balls he plays. The probability that in a given throw he does not hit the boundary is | P (E ) +P (not E) =1 |
Each question consists of two statements, namely, Assertion(A) and Reason (R) . Choose the correct options.
Assertion (A) | Reason (R) |
The probability of a sure event is 1. | Let E be an event. Then 0<P (E ) <1. |
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 students is chosen at random.
What is the probability that the chosen student
(i) gets 20% or less marks?
(ii) gets 60% or more marks?
The table given below shows the ages of 75 teachers in a school.
Age (in years) | 18-29 | 30-39 | 40-49 | 50-59 |
No of teachers | 5 | 25 | 35 | 10 |
Note Here 18-29 means from 18 to 29 including both. A teacher from the school is chosen at ramdom. What is the probability that the teacher chosen is
(i) 40 years or more then 40 years old?
(ii) 49 years or less then 49 years old?
(iii) 60 years or more then 60 years old?
A die is thrown 80 times and the outcomes were noted as under:
Outcomes | 1 | 2 | 3 | 4 | 5 | 6 |
Frequency | 14 | 11 | 9 | 13 | 18 | 15 |
If the die is thrown at random, What is the probability of getting a 2?
Two coins are tossed simultaneously 80 times and the outcomes were recorded as under:
Outcome | Two heads | One head | No head |
Frequency | 24 | 36 | 20 |
If two coins are tossed at random,find the probability of getting
(i) Two heads (ii) one head (iii) no head
Marks obtained by 90 students of Class IX in a test are given below:
Marks | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
No of students | 8 | 15 | 32 | 26 | 9 |
Out of these students one is chosen at random. Find the probability that the chosen student obtains
(i) less than 20% marks (ii) 80% of more marks
(iii) 60% or more marks
The blood group of 30 students of a class were recorded as under:
Blood Group | A | B | AB | O |
No of students | 9 | 11 | 4 | 6 |
If a students of this class is chosen at random, What is the probability that the chosen students has blood group
(i)0? (ii) A? (iii) AB?
In a survey of 100 families having 2 or less boys. The following data was obtained:
Number of boys in a family | 0 | 1 | 2 |
Number of families | 18 | 46 | 36 |
If one of the given families is chosen at random, what is the probability that the chosen family has
(i) 1 boy? (ii) 2 boys? (iii) no boy?
A die is thrown 100 times and following observations were recorded:
Outcomes | 1 | 2 | 3 | 4 | 5 | 6 |
Frequency | 12 | 18 | 14 | 26 | 14 | 16 |
If a die is thrown at random, find the probability of getting
(i) a number less than 3? (ii) a number greater than 4 (iii) an even number
A survey of 600 students about their liking on coffee was conducted and recoded as under:
Opinion | Like | Dislike |
No of students | 360 | 140 |
Out of these students one is chosen at random. What is the probability that the chosen student
(i) likes coffee? (ii) dislikes coffee?
Two coins are tossed 1000 times and the outcomes are recorded as given below:
Number of heads | 0 | 1 | 2 |
Frequency | 240 | 450 | 310 |
In a simple throw of two coins, what is the probability of getting
(i) at most one head? (ii) At least one head?