Probability (MATHEMATICS) – 9th Class
TEXTBOOK QUESTIONS SOLVED
1. In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.
2. 1500 families with 2 children were selected randomly, and the following data were recorded:
|Number of girls in a family||2||1||0|
|Number of families||475||814||211|
Compute the probability of a family, chosen at random, having
(i) 2 girls (ii) 1 girl (iii) No girl.
Also check whether the sum of these probabilities is 1.
3. In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data, so obtained:
Observe the bar graph given above and then find the probability that a student of the class was born in August.
4. Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:
|Outcome||3 heads||2 heads||1 heads||No head|
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.
5. An organisation selected 2400 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:
Suppose a family is chosen. Find the probability that the family chosen is
(i) earning Rs.10000-13000 per month and owning exactly 2 -vehicles,
(ii) earning Rs.16000 or Mom per month and owning exactly 1 vehicle.
(iii) earning less than Rs.7000 per month and does not own any vehicle.
(iv) earning Rs.13000-16000 per month and owning more than 2 vehicles.
(v) owning not more than 1 vehicle.
6. A teacher wanted to analys, the performance of two sections of students in Mathematics out of 100 marks. Looking at their performances, she found that a few students got under 20 marks and a kw got 70 marks or above. So she decided to group them into internals of varying sizes as follows: 0-20, 20-30,……., 60-70, 70-100.
Then she formed the following table:
|Marks||Number of students|
(i) Find the probability that a student obtained less than 20% in the mathematics test.
(ii) Find the probability that a student obtained marks 60 or above.
7. To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table.
|Opinion||Number of students|
Find the probability that a student chosen at random
(i) likes statistics, (ii) does not like it.
8. The distance (in km) of 40 engineers from their residence to their place of work were found as follows:
5 3 10 20 25 11 13 7 12 31
19 10 12 17 18 11 32 17 16 2
7 9 7 8 3 5 12 15 18 3
12 14 2 9 6 15 15 7 6 12
What is the empirical probability that an engineer lives:
(i) less than 7 km from her place of work?
(ii) more than or equal to 7 km from her place of work?
(iii) within km from her place of work?
9. Activity: Note the frequency of two-wheelers, three-wheelers and four-wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two-wheeler
10. Activity: Ask all the students in your class to write a 3-digit number in order. Choose any student from the room random. What is the probability that the number written by her /him is divisible by 3? Remember that a number is divisible by 3. if the some of its digits is divisible by 3.
11. Eleven bags of wheal flour, each marked 5 kg, actually contained the following weights of flour
4.97 5.05 5.08 5.03 5.00 5.06 5.08 4.98 5.04 5.07 5.00
Find the probability that any of these bags chosen at random contains more than 5 kg of flow:
12. A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The frequency distribution table obtained for 30 days is as follows:
|Concentration of sulphur dioxide (in ppm)||Frequency|
|Total = 30|
Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12-0.16 on any of these days.
13. The blood group of 30 students of Class IX are recorded. The table obtained fbr 30 students is as following:
|Blood group||Number of students|
|Total = 30|
Use the table to determine the probability that a student of this class, selected at random has blood group AB.