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प्रश्न
Which of the following cannot be the probability of an event?
विकल्प
`1/3`
`3/5`
`5/3`
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.
All the options except (c) satisfy the above criteria’s.
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संबंधित प्रश्न
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.
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
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Also check whether the sum of these probabilities is 1.
An organization 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:-
|
Monthly income (in Rs.) |
Vehicles per family | |||
| 0 | 1 | 2 | Above 2 | |
| Less than 7000 | 10 | 160 | 25 | 0 |
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| 10000 – 13000 | 1 | 535 | 29 | 1 |
| 13000 – 16000 | 2 | 469 | 59 | 25 |
| 16000 or more | 1 | 579 | 82 | 88 |
Suppose a family is chosen, find the probability that the family chosen is
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(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 vehicles.
(v) owning not more than 1 vehicle.
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| Opinion | Number of students |
| like | 135 |
| dislike | 65 |
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Define an event.
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A company selected 4000 households at random and surveyed them to find out a relationship between income level and the number of television sets in a home. The information so obtained is listed in the following table:
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| 0 | 1 | 2 | Above 2 | |
| < 10000 | 20 | 80 | 10 | 0 |
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| 25000 and above | 0 | 1100 | 760 | 220 |
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- of a household earning Rs 25000 and more per year and owning 2 televisions.
- of a household not having any television.
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| Age (in years) | 20 – 29 | 30 – 39 | 40 – 49 | 50 – 59 | 60 and above |
| Number of workers | 38 | 27 | 86 | 46 | 3 |
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| Age (in years) | 20 – 29 | 30 – 39 | 40 – 49 | 50 – 59 | 60 and above |
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