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प्रश्न
Which of the following cannot be the probability of an event?
पर्याय
`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
Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg):- 4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00
Find the probability that any of these bags chosen at random contains more than 5 kg of flour.
Two coins are tossed simultaneously 500 times with the following frequencies of different outcomes:
Two heads: 95 times
One tail: 290 times
No head: 115 times
Find the probability of occurrence of each of these events.
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.
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.
Define an event.
A die is thrown 100 times. If the probability of getting an even number is `2/5` . How many times an odd number is obtained?
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 between 8 and 12?
Over the past 200 working days, the number of defective parts produced by a machine is given in the following table:
| Number of defective parts |
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| Days | 50 | 32 | 22 | 18 | 12 | 12 | 10 | 10 | 10 | 8 | 6 | 6 | 2 | 2 |
Determine the probability that tomorrow’s output will have not more than 5 defective parts
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
