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प्रश्न
The probability an event of a trial is
विकल्प
1
0
less than 1
more than 1
उत्तर
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 m is always less than or equal to n and n is a positive integers, it can’t be zero. But, m is a non negative integer. So, the maximum value of probability of an event is `n/n=1`, which is the probability of a certain event and the minimum value of it is 0, which is the probability of an impossible event. For any other events the value is in between 0 and 1.
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संबंधित प्रश्न
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:-
Find the probability that a student of the class was born in August.
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 |
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.
Mark the correct alternative in each of the following:
The probability of an impossible event is
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 medical examination of students of a class, the following blood groups are recorded:
| Blood group | A | AB | B | O |
| Number of students | 10 | 13 | 12 | 5 |
A student is selected at random from the class. The probability that he/she has blood group B, 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 less than or equal to 5?
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?
