Question

Of the students in a school 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?

Answer 1

Let $E_1:$Students having 100% attendance,

$E_2:$ Students not having 100% attendance

And so $p\left(E_1\right)=\frac{30}{100}$

$p\left(A/E_1\right)\frac{70}{100}$

$P\left(A/E_1\right)=\frac{10}{100}$

By boy’s theoxm,

$p\left(E_1/A\right)=\frac{p\left(E_1\right)p\left(A/E_1\right)}{p\left(E_1\right)p\left(A/E_1\right)+p\left(E_2\right)p\left(A/E_2\right)}$

$=\frac{\frac{30}{100}\times \frac{70}{100}}{\frac{30}{100}\times \frac{70}{100}+\frac{70}{100}\times \frac{10}{100}}$

$=\frac{21}{28}$

$=\frac{3}{4}$