notes
The likelihood of something happening is called the probability.
Terms related to probability:
Experiment : An activity which produces an outcome or result is called an experiment.
random Experiment : An Experiment in which exact outcome cannot be predicted in advance.
For example:
1) rolling a dice
2) Drawing a card from well-shuffled pack of playing cards
3) Tossing a coin
Trial : Performing an experiment is called a trial.
Event : Each possible outcomes of an experiment is called event.
Probability of an event : In a random experiment if 'n' is the total number of trials, then the empirical probability of the event E is P(E).
P(E) =
`"Number of trials happened in which event happened" / " Total number of trials"`
i.e. P(E) =`"Number of trials happened in which event happened" / n `
The Probability of an event lies between 0 and 1 (0 and 1 inclusive).
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Related QuestionsVIEW ALL [43]
To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table.
| Opinion | Number of students |
| like | 135 |
| dislike | 65 |
Find the probability that a student chosen at random
(i) likes statistics, (ii) does not like it
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.
| 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.
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
(i) 2 girls (ii) 1 girl (iii) No girl
Also check whether the sum of these probabilities is 1.
| Concentration of SO2 (in ppm) | Number of days (Frequency) |
| 0.00 − 0.04 | 4 |
| 0.04 − 0.08 | 9 |
| 0.08 − 0.12 | 9 |
| 0.12 − 0.16 | 2 |
| 0.16 − 0.20 | 4 |
| 0.20 − 0.24 | 2 |
| Total | 30 |
The above frequency distribution table represents the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12 − 0.16 on any of these days.
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.
