Question

In a class 35% of the student are poor. 20% are meritorious and 15% are both poor and meritorious. one student is selected at random. find the probability that (i) he is poor if it is know that he meritorious.
(II) he is meritorious if it is know that he is poor.

Answer 1

Let the poor student $P\left(A\right)=35$

Meritorious student $P\left(B\right)=20$

Both $P(A\cap B)=15$

Now,

$P\left(A\right)=\frac{35}{100}$

$P\left(B\right)=\frac{20}{100}$

$P(A\cap B)=\frac{15}{100}$

(a).He is poor if it is know that he meritorious

Probability

$P\left(\frac{A}{B}\right)=\frac{P(A\cap B)}{P\left(B\right)}=\frac{\frac{15}{100}}{\frac{20}{100}}$

$P\left(\frac{A}{B}\right)=\frac{15}{20}$

$P\left(\frac{A}{B}\right)=\frac{3}{4}$

(a).He is meritorious if it is know that he poor

Probability

$P\left(\frac{B}{A}\right)=\frac{P(A\cap B)}{P\left(A\right)}=\frac{\frac{15}{100}}{\frac{35}{100}}$

$P\left(\frac{A}{B}\right)=\frac{15}{35}$

$P\left(\frac{A}{B}\right)=\frac{5}{7}$

Hence, this is the answer.