1. In an ODI match, a wicket keeper drops a catch 6 times out of 30 catches he gets. Find the probability of the wicketkeeper not dropping a catch.
Sol: Let E be the event of dropping a catch
P(E)= Probability of the wicketkeeper dropping a catch =
Thus, Probability of not dropping a catch is 1-P(E) =
2. 1500 families with 2 children were selected randomly, and the following data were recorded:
|No of girls in a family||2||1||0|
|No of families||500||300||200|
What is the probability that a family, chosen at random, has
i. 2 girls
ii. 1 girl
iii. No girl
Also check whether the sum of these probabilities is 1.
Sol: Total number of families =
i. P(Probability of 2 girls) =
ii. P(Probability of 1 girl) =
iii. P(Probability of No girl) =
Sum of all Probabilities =
3. From the following table, Find the probability of a student selected at random being born in April.
|No of students||5||6||4||2||8||1||5||4||4||3||7||1|
Sol: Total number of students:
P( Student born in April) =
4. Three coins are tossed simultaneously 210 times with the following frequencies of different outcomes:
|Outcome||3 Heads||2 Heads||1 Head||No Head|
If the three coins are simultaneously tossed again, What is the probability of not getting even a single head?
Sol: Number of times the coins were tossed = 210
P( Not getting even a single head) =
5. An organization selected 1900 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:
Vehicles per family
|Income level||0||1||2||More than 2|
|Less than 6000||10||60||25||0|
|6000 to 11000||0||205||27||2|
|11000 to 14000||1||435||29||1|
|14000 to 17000||2||369||59||25|
|17000 or more||1||479||82||88|
Find the probability that a family chosen at random is
(i) Earning 11000 – 14000 per month and owning exactly 1 vehicle.
(ii) Earning 17000 or more per month and owning exactly 2 vehicles.
(iii) Earning less than 6000 per month and does not own any vehicle.
(iv) Earning 6000-11000 per month and owning more than 2 vehicles
(v) Owning more than 2 vehicles
Sol: Total number of families: 1900
- P( Earning 11000-14000 and owning 1 vehicle) =
- P( Earning 17000 or more and owning 2 vehicles) =
- P( Earning less than 6000 and doesn’t own any vehicle) =
- P( Earning 6000-11000 and owning more than 2 vehicles) =
- P( Owning more than 2 vehicles) =
6. In a science test, the marks of 100 students of class VI are listed in the following table:
(Out of 100)
|No of students|
i. What is the probability that a student selected at random has scored less than 40?
ii. What is the probability that a student selected at random has scored more than 50?
Sol: Total number of students = 100
Number of students having scored less than 40% =
Number of students having scored more than 50% =
i. P(Less than 40%) =
ii. P(More than 50%) =
7. The distance (in km) of 20 doctors from their residence to their place of work were found as follows:
5, 6, 4, 7, 2, 9, 1, 6, 4, 3, 5, 32, 4, 6, 21, 15, 4,15,18,5
What is the probability that a doctor lives:
(i) Less than 6 km from her place of work?
(ii) More than or equal to 6 km from her place of work?
(iii) Within 0.5 km from her place of work?
Sol: Total number of doctors = 20
Number of doctors with travelling distance below 6km = 10
Number of doctors with travelling distance more than or equal to 6 km = 10
Number of doctors with travelling distance below 0.5 km = 0
(i) P( Less than 6 km) =
(ii) P( More than or equal to 6) =
(iii) P(Less than 0.5 km) =
8. A survey of 100 students was conducted to know the opinion of the students about the subject statistics which is recorded in the following table.
|Opinion||Number of students|
What is the probability that a student selected at random
i. Likes the subject?
ii. Dislikes the subject?
Sol: Total number of students = 100
Number of students liking the subject = 37
Number of students disliking the subject = 63
i. P(liking the subject) =
ii. P(Disliking the subject) =
9. Nine bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg):
5.08 ,4.95, 5.00, 4.96, 5.08, 4.98, 5.04, 5.07 and 5.00
What is the probability that any of these bags chosen at random contains less than 5 kg of flour?
Sol: Total number of wheat bags = 9
Number of wheat bags weighing less than 5 kg = 3
P( Weighing less than 5 kg) =
10. You were asked to prepare a frequency distribution table regarding the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class, selected at random, has blood group AB.
The blood groups of 10 students of Class VIII are recorded as follows:
O,AB,A,B,O,A,AB,AB,O and AB
Represent this data in the form of a frequency distribution table. Use this table to determine the probability that a student of this class, selected random, has blood group O.
Sol: Frequency Distribution Table:
Total number of students = 10
Number of students having blood group O = 3
P(Blood group O) =