Question

Neither physics nor chemistry

• A. $0.23$
• B. $0.22$
• C. $0.21$
• D. $0.20$

Answer 1

Answer: (A)

$0.23$

Given, In a class $100$ students out of which $45$ study mathematics, $48$ study physics, $40$ study chemistry, $12$ study both maths and physics, $11$ study both physics and chemistry, $15$ study both mathematics and chemistry and $5$ study all the subjects.
$\Rightarrow n\left(\mu \right)=100,n\left(M\right)=45,n\left(P\right)=48,n\left(C\right)=40,n(M\cap P)=12,n(P\cap C)=11,n(C\cap M)=15,n(M\cap P\cap C)=5$
Student studies neither physics nor chemistry,$n\left(X\right)=\left(n\right(M)-n(M\cap C)-n(M\cap P)+n(M\cap P\cap C)$$=(45-15-12+5)=23$
The required probability$=\frac{n\left(X\right)}{n\left(\mu \right)}=\frac{23}{100}=0.23$