in a class of 40 student,18 pass maths, 19 pass account,16 pass economics 5 pass maths and account only, 6 pass maths only, if each student pass at least one of the subject.find the percentage number who fail in at least one of economics and maths. how many student fail in all the three subject.calculate the probability that a student selected at random fail in account
To find the percentage of students who fail in at least one of economics and maths, we need to count the number of students who do not pass either of these subjects.
Step 1: Calculate the number of students who pass both maths and account:
To find this, subtract the number of students who only pass maths and account from the total number of students who pass both maths and account.
5 students pass maths and account only (given).
18 - 5 = 13 students pass both maths and account.
Step 2: Calculate the number of students who pass only maths:
To find this, subtract the number of students who pass both maths and account, students who only pass economics, and students who pass all three subjects from the total number of students who pass maths.
6 students pass maths only (given).
13 (students pass both maths and account) + unknown (students who pass all three subjects) + 6 (students pass maths only) = 18 (students pass maths).
So, the number of students who pass all three subjects is 18 - 13 - 6 = -1.
Since we cannot have a negative number of students, this result is not possible.
Therefore, there are no students who pass all three subjects.
Step 3: Calculate the number of students who fail in at least one of economics and maths:
To find this, subtract the number of students who pass both maths and account (13) from the total number of students (40).
40 - 13 = 27 students fail in at least one of economics and maths.
Step 4: Calculate the percentage of students who fail in at least one of economics and maths:
To find this percentage, divide the number of students who fail in at least one of economics and maths by the total number of students, and then multiply by 100.
(27 / 40) * 100 = 67.5%
Now, to calculate the probability that a student selected at random fails in account:
Step 5: Calculate the number of students who fail in account:
To find this, subtract the number of students who pass account (19) from the total number of students (40).
40 - 19 = 21 students fail in account.
Step 6: Calculate the probability:
To calculate the probability of a student selected at random failing in account, divide the number of students who fail in account by the total number of students.
21 / 40 = 0.525 (or 52.5%)
So, the probability that a student selected at random fails in account is 0.525 (or 52.5%).