Question

In a college, $70$% students pass in Physics, $75$% pass in Mathematics and $10$% students fail in both. One student is chosen at random. What is the probability that:
He passes in Physics given that he passes in Mathematics

Answer 1

Let $x$% students pass in both
Students who pass in Physics $=70$% $\Rightarrow P\left(P\right)=\frac{70}{100}$
Students who pass in Maths $=75$% $\Rightarrow P\left(M\right)=\frac{75}{100}$
Students who fail in both $=10$%
$70$% $-x+x+75$% $-x=90$%
$x=55$% $\Rightarrow P(M\cap P)=\frac{55}{100}$
$P\left(\frac{P}{M}\right)=\frac{P(M\cap P)}{P\left(M\right)}$
$=\frac{55/100}{75/100}$
$=\frac{55}{75}=\frac{11}{15}$