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प्रश्न
Define an event.
उत्तर
What are the meanings of event?
The word event means something that result.
Definition:
An event is a collection of outcomes of a trial of a random experiment.
To illustrate the definition, let us take examples:
1. When two coins are tossed simultaneously, the possible outcomes are HH, HT, TH and TT. Any one outcome like HH is called an event (elementary event). The collections like {HH, HT}, {HH, HT, TT} etc are all events (compound event).
2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Any one outcome like 4 is called an event (elementary event). The collections like {1, 2}, {1, 2, 3}, {2, 5, 6}, {2, 3, 4, 5} etc are all events (compound events).
Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.
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संबंधित प्रश्न
A teacher wanted to analyse the performance of two sections of students in a mathematics test of 100 marks. Looking at their performances, she found that a few students got under 20 marks and a few got 70 marks or above. So she decided to group them into intervals of varying sizes as follows: 0 − 20, 20 − 30… 60 − 70, 70 − 100. Then she formed the following table:-
| Marks | Number of students |
| 0 - 20 | 7 |
| 20 - 30 | 10 |
| 30 - 40 | 10 |
| 40 - 50 | 20 |
| 50 - 60 | 20 |
| 60 - 70 | 15 |
| 70 - above | 8 |
| Total 90 | |
(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.
The percentage of marks obtained by a student in monthly unit tests are given below:
| Unit test: | I | II | III | IV | V |
| Percentage of marks obtained: | 69 | 71 | 73 | 68 | 76 |
Find the probability that the student gets:
(i) more than 70% marks
(ii) less than 70% marks
(iii) a distinction
Following table shows the birth month of 40 students of class IX.
| Jan | Feb | March | April | May | June | July | Aug | Sept | Oct | Nov | Dec |
| 3 | 4 | 2 | 2 | 5 | 1 | 2 | 5 | 3 | 4 | 4 | 4 |
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.
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.
A big contains 4 white balls and some red balls. If the probability of drawing a white ball from the bag is `2/5`, find the number of red balls in the bag.
Bulbs are packed in cartons each containing 40 bulbs. Seven hundred cartons were examined for defective bulbs and the results are given in the following table:
| Number of defective bulbs | 0 | 1 | 2 | 3 | 4 | 5 | 6 | more than 6 |
| Frequency | 400 | 180 | 48 | 41 | 18 | 8 | 3 | 2 |
One carton was selected at random. What is the probability that it has
- no defective bulb?
- defective bulbs from 2 to 6?
- defective bulbs less than 4?
Bulbs are packed in cartons each containing 40 bulbs. Seven hundred cartons were examined for defective bulbs and the results are given in the following table:
| Number of defective bulbs | 0 | 1 | 2 | 3 | 4 | 5 | 6 | more than 6 |
| Frequency | 400 | 180 | 48 | 41 | 18 | 8 | 3 | 2 |
One carton was selected at random. What is the probability that it has defective bulbs from 2 to 6?
A recent survey found that the ages of workers in a factory is distributed as follows:
| Age (in years) | 20 – 29 | 30 – 39 | 40 – 49 | 50 – 59 | 60 and above |
| Number of workers | 38 | 27 | 86 | 46 | 3 |
If a person is selected at random, find the probability that the person is having age from 30 to 39 years
A recent survey found that the ages of workers in a factory is distributed as follows:
| Age (in years) | 20 – 29 | 30 – 39 | 40 – 49 | 50 – 59 | 60 and above |
| Number of workers | 38 | 27 | 86 | 46 | 3 |
If a person is selected at random, find the probability that the person is under 60 but over 39 years
