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प्रश्न
Define probability of an event.
उत्तर
The probability of an event denotes the relative frequency of occurrence of an experiment’s outcome, when repeating the experiment.
Definition:
The empirical or experimental definition of probability is that 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 probability of happening of event A is denoted by P (A) and is given by
` P(A) = m/n`
To illustrate the definition, let us take examples:
1. When two coins are tossed simultaneously, the possible outcomes are HH, HT, TH and TT. The total number of trials is 4. Let A be the event of occurring exactly two heads. The number of times A happens is 1. So, the probability of the event A is
` P(A) = m/n`
`=1/4`
= 0 . 25
2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Let A be the event of occurring a number greater than 3. The total number of trials is 6. The number of times A happens is 3. So, the probability of the event A is
` P(A) = m/n`
` = 3/6 `
`=1/2`
= 0. 5
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
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.
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 |
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.
Three coins are tossed simultaneously 100 times with the following frequencies of different outcomes:
| Outcome: | No head | One head | Two heads | Three heads |
| Frequency: | 14 | 38 | 36 | 12 |
If the three coins are simultaneously tossed again, compute the probability of:
(i) 2 heads coming up.
(ii) 3 heads coming up.
(iii) at least one head coming up.
(iv) getting more heads than tails.
(v) getting more tails than heads.
1500 families with 2 children were selected randomly and the following data were recorded:
| Number of girls in a family | 0 | 1 | 2 |
| Number of families | 211 | 814 | 475 |
(i) No girl
(ii) 1 girl
(iii) 2 girls
(iv) at most one girl
(v) more girls than boys
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.
Define an event.
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.
In a survey of 364 children aged 19 – 36 months, it was found that 91 liked to eat potato chips. If a child is selected at random, the probability that he/she does not like to eat potato chips is ______.
Two coins are tossed 1000 times and the outcomes are recorded as below:
| Number of heads | 2 | 1 | 0 |
| Frequency | 200 | 550 | 250 |
Based on this information, the probability for at most one head 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?
