RD Chapter 25 Probability Ex 25.1 Solutions
Question - 11 : - Given below is the frequency distribution table regarding the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days.
| Conc. of SO2 | 0.00-0.04 | 0.04-0.08 | 0.08-0.12 | 0.12-0.16 | 0.16-0.20 | 0.20-0.24 |
| No. days: | 4 | 8 | 9 | 2 | 4 | 3 |
Find the probability of concentration of sulphur dioxide in the interval
0.12-0.16 on any of these days.
Answer - 11 : -
The total number of trials is 30.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by
and is given by Let A1 be the event that the concentration of sulphur dioxide in a day is 0.12-0.16 parts per million.
The number of times A1 happens is 2.
Therefore, we have
Question - 12 : - A company selected 2400 families at random and survey them to determine a relationship between income level and the number of vehicles in a home. The information gathered is listed in the table below: | Monthly income:
(in Rs) | Vehicles per family |
| 0 | 1 | 2 | Above 2 |
| Less than 7000
7000-10000
10000-13000
13000-16000
16000 or more | 10
0
1
2
1 | 160
305
535
469
579 | 25
27
29
29
82 | 0
2
1
25
88 |
If a family is chosen, find the probability that family is:
(i) earning Rs10000-13000 per month and owning exactly 2 vehicles.
(ii) earning Rs 16000 or more 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 vehicle.
(v) owning not more than 1 vehicle
(vi) owning at least one vehicle.
Answer - 12 : -
The total number of trials is 2400.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by (i) Let A1 be the event that a chosen family earns Rs 10000-13000 per month and owns exactly 2 vehicles.
The number of times A1 happens is 29.
Therefore, we have
(ii) Let A2 be the event that a chosen family earns Rs 16000 or more per month and owns exactly 1 vehicle.
The number of times A2 happens is 579.
Therefore, we have
(iii) Let A3 be the event that a chosen family earns less than Rs 7000 per month and does not owns any vehicles.
The number of times A3 happens is 10.
Therefore, we have
(iv) Let A4 be the event that a chosen family earns Rs 13000-16000 per month and owns more than 2 vehicles.
The number of times A4 happens is 25.
Therefore, we have
(v) Let A5 be the event that a chosen family owns not more than 1 vehicle (may be 0 or 1). In this case the number of vehicles is independent of the income of the family.
The number of times A5 happens is
.
Therefore, we have
(vi) Let A6 be the event that a chosen family owns atleast 1 vehicle (may be 1 or 2 or above 2). In this case the number of vehicles is independent of the income of the family.
The number of times A6 happens is
.
Therefore, we have
The following table gives the life time of 400 neon lamps:
| Life time
(in hours) | 300-400 | 400-500 | 500-600 | 600-700 | 700-800 | 800-900 | 900-1000 |
| Number of lamps: | 14 | 56 | 60 | 86 | 74 | 62 | 48 |
A bulb is selected of random, Find the probability that the the life time of the selected bulb is:
(i) less than 400
(ii) between 300 to 800 hours
(iii) at least 700 hours.
Answer - 13 : -
The total number of trials is 400.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by (i) Let A1 be the event that the lifetime of a chosen bulb is less than 400 hours.
The number of times A1 happens is 14.
Therefore, we have
(ii) Let A2 be the event that the lifetime of a chosen bulb is in between 300 to 800 hours.
The number of times A2 happens is 
. Therefore, we have
. (iii) Let A3 be the event that the lifetime of a chosen bulb is atleast 700 hours.
The number of times A3 happens is 
. Therefore, we have
Given below is the frequency distribution of wages (in Rs) of 30 workers in a certain factory:
| Wages (in Rs) | 110-130 | 130-150 | 150-170 | 170-190 | 190-210 | 210-230 | 230-250 |
| No. of workers | 3 | 4 | 5 | 6 | 5 | 4 | 3 |
A worker is selected at random. Find the probability that his wages are:
(i) less than Rs 150
(ii) at least Rs 210
(iii) more than or equal to 150 but less than Rs 210.
Answer - 14 : -
The total number of trials is 30.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by (i) Let A1 be the event that the wages of a worker is less than Rs 150.
The number of times A1 happens is
. Therefore, we have
.(ii) Let A2 be the event that the wages of a worker is atleast Rs 210.
The number of times A2 happens is 
. Therefore, we have
.(iii) Let A3 be the event that the wages of a worker is more than or equal to Rs 150 but less than Rs 210.
The number of times A3 happens is 
. Therefore, we have