#### Question

Of the students in a school, it is known that 30% have 100% attendance and 70% students are irregular. Previous year results report that 70% of all students who have 100% attendance attain A grade and 10% irregular students attain A grade in their annual examination. At the end of the year, one student is chos~n at random from the school and he was found ·to have an A grade. What is the probability that the student has 100% attendance? Is regularity required only in school? Justify your answer

#### Solution

Let `E_1` is event of students which have 100% attendance and `E_2` is event of students which are Irregular

then `P(E_1) = 0.3`

`P(E_2) = 0.7`

Let A : Event of students which attendance A grade

then P(A/ E_{1}) = 0.7 and P(A/ E_{2}) = 0.1

So By Bays theorem

P(Probability that student has 100% Attendance)

As per answer, the probability of regular students is more than 50%. So the regularty is required.