Question

In a college, 30% students fail in physics, 40% fail in mathematics and 20% fail in both. One student is chosen at random. The probability that she fails in mathematics if she has failed in physics is

• A. $\frac{2}{3}$
• B. $\frac{3}{4}$
• C. $\frac{1}{2}$
• D. 1

Answer 1

The correct option is A $\frac{2}{3}$

$\mathrm{Let}\mathrm{us}\mathrm{define}\mathrm{the}\mathrm{following}\mathrm{events}:A:‘\mathrm{the}\mathrm{student}\mathrm{fails}\mathrm{in}\mathrm{mathematics}\text{'}.B:‘\mathrm{the}\mathrm{student}\mathrm{fails}\mathrm{in}\mathrm{physics}\text{'}.\mathrm{Given}P\left(A\right)=0.4,P\left(B\right)=0.3\mathrm{and}P\left(A\cap B\right)=0.2\mathrm{We}\mathrm{need}\mathrm{to}\mathrm{find}P\left(A|B\right).\mathrm{By}\mathrm{conditional}\mathrm{probability},P\left(A|B\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}\Rightarrow P\left(A|B\right)=\frac{0.2}{0.3}\Rightarrow P\left(A|B\right)=\frac{2}{3}$