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 chosen 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.

Answer 1

Let E:the student has grade A,$E_1$ :the student has 100% attendance and $E_2$ :the student is irregular.

Clearly P$\left(E_1\right)$ =30%,P$\left(E_2\right)$=70%,P$\left(E|E_1\right)$=70% and P$\left(E|E_2\right)$=10%

By Bayes' Theorem,$P\left(E_1|E\right)=\frac{P\left(E|E_1\right)P\left(E_1\right)}{P\left(E|E_1\right)P\left(E_1\right)+P\left(E|E_2\right)P\left(E_2\right)}=\frac{70\times 30}{70\times 30+10\times 70}=\frac{3}{4}$=75%.

The value of Regularity helps in all aspects of life.Regularity in school as well as professional life brings success for us.