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.
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).
`"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).
Shaalaa.com | Probability Experimental Approach
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|
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|
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.
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.
|Blood Group||Number of Students|
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|
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.
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.
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|
(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.