Question

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	No. of Students
Like	135
Dislike	65

Find the probability that a student chosen at random
(i) Likes statistics
(ii) Does not like it

Answer 1

Hint: To find out the probability of a desired outcome we are provided with the formulae
P(A) =n(E)/n(S)
Where,
P(A) = Probability of an event
n(E) = Number of desired outcome
n(S) = Total number of outcomes
We will make use of the formula and find out the values for the particular conditions given


Complete step by step explanation:
Case (i): Students who like statistics
1. Total number of students = 200
i.e. n(S), which is total number of outcomes = 200
2. Students who likes statistics =135
i.e. n(E), which is desired outcome = 135
3. P(A) is the probability of students who like statistics
Using formulae P(A) = n(E)/n(S)
And putting the values of n(E) and n(S) from step 1 and step 2
P(A) = $\dfrac{{135}}{{200}}$
P(A) Probability of student who likes statistics = $\dfrac{{135}}{{200}}$
Case (ii): Students who does not like statistics
4. Total number of students = 200
i.e. n(S), which is total number of outcomes = 200
5. Students who does not like statistics = 65
i.e. n(E), which is desired outcome = 65
6. P(A) is the probability of students who like statistics
Using formulae P(A) = n(E)/n(S)
And putting the values of n(E) and n(S) from step 4 and step 5
P(A) = $\dfrac{{65}}{{200}}$
P(A) Probability of students who does not like statistics = $\dfrac{{65}}{{200}}$
Note: Point to be noted that in case a student want to verify their answers that the probability of the students who like and who doesn’t like statistics can be easily find out by simply adding both the probabilities and it will be equal to one because the sum of probabilities of all the events happening should be equal to one, then our solution is right.