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प्रश्न
Mark the correct alternative in each of the following:
The probability of an impossible event is
विकल्प
1
0
less than 0
greater than 1
उत्तर
We have to find the probability of an impossible event.
Note that the number of occurrence of an impossible event is 0. This is the reason that’s why it is called impossible event.
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 P (A) and is given by
` P(A) = m/n`
Note that n is a positive integer, it can’t be zero. So, whatever may be the value of n, the probability of an impossible event is `0/n=0`.
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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.
| Blood Group | Number of Students |
| A | 9 |
| B | 6 |
| AB | 3 |
| O | 12 |
| Total | 30 |
The above frequency distribution table represents 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 30 students of class IX are recorded as follows:
| A | B | O | O | AB | O | A | O | B | A | O | B | A | O | O |
| A | AB | O | A | A | O | O | AB | B | A | O | B | A | B | O |
(i) A
(ii) B
(iii) AB
(iv) O
Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:
| Outcome | 3 heads | 2 heads | 1 head | No head |
| Frequency | 23 | 72 | 77 | 28 |
Find the probability of getting at most two heads.
A dice is rolled 600 times and the occurrence of the outcomes 1, 2, 3, 4, 5 and 6 are given below:
| Outcome | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 200 | 30 | 120 | 100 | 50 | 100 |
The probability of getting a prime number is
In a football match, Ronaldo makes 4 goals from 10 penalty kicks. The probability of converting a penalty kick into a goal by Ronaldo, is
In a sample study of 642 people, it was found that 514 people have a high school certificate. If a person is selected at random, the probability that the person has a high school certificate is ______.
Two dice are thrown simultaneously 500 times. Each time the sum of two numbers appearing on their tops is noted and recorded as given in the following table:
| Sum | Frequency |
| 2 | 14 |
| 3 | 30 |
| 4 | 42 |
| 5 | 55 |
| 6 | 72 |
| 7 | 75 |
| 8 | 70 |
| 9 | 53 |
| 10 | 46 |
| 11 | 28 |
| 12 | 15 |
If the dice are thrown once more, what is the probability of getting a sum
- 3?
- more than 10?
- less than or equal to 5?
- between 8 and 12?
Two dice are thrown simultaneously 500 times. Each time the sum of two numbers appearing on their tops is noted and recorded as given in the following table:
| Sum | Frequency |
| 2 | 14 |
| 3 | 30 |
| 4 | 42 |
| 5 | 55 |
| 6 | 72 |
| 7 | 75 |
| 8 | 70 |
| 9 | 53 |
| 10 | 46 |
| 11 | 28 |
| 12 | 15 |
If the dice are thrown once more, what is the probability of getting a sum less than or equal to 5?
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
