Question

In a science talent examination, 50% of the candidates fail in Mathematics and 50% fail in Physics. If 20% fail in both these subjects, then the percentage who pass in both Mathematics and Physics is:

• A. 0%
• B. 20%
• C. 25%
• D. 50%

Answer 1

The correct option is B 20%

By set theory

$n(M\cup P)=n\left(M\right)+n\left(P\right)-n(M\cap P)$ where M and P are sets of students failing in respective subjects.

$=0.5+0.5-0.2=0.8$

This indicates $80\%$ of the class fails in at least one of the given subjects while $20\%$ pass in both.