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:
(i) He passes in Physics and Mathematics.
(ii) He passes in Mathematics given that he passes in Physics.
(iii) 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 $=10$%
$70$% $-x+x+75$% $-x=90$%
$x=55$% $\Rightarrow P(M\cap P)=\frac{55}{100}$
$P$ (Passes in Physics and Mathematics) $=\frac{55}{100}=\frac{11}{20}$