Question

In a class of 125 students 70 passed in Mathematics, 55 in Statistics and 30 in both. The probability that a student selected at random from the class, has passed in only one subject is

• A. $\frac{13}{25}$
• B. $\frac{3}{25}$
• C. $\frac{17}{25}$
• D. $\frac{8}{25}$

Answer 1

The correct option is A $\frac{13}{25}$

Let the given equation be

$n\left(M\right)=70$( students passed in mathematics) ;

$n\left(S\right)=55$( students passed in Statistics) ;

$n\left(M\cap S\right)=30$

Therefore, probability of students passed in mathematics $=\frac{70}{125}$

Probability of students passed in statistics $=\frac{55}{125}$

Implies that, $P\left(M\cup S\right)=P\left(M\right)+P\left(S\right)-P\left(M\cap S\right)$

Implies that, $P(M\cup S)=\frac{70}{125}+\frac{55}{125}-\frac{30}{125}$

Hence the result is $=\frac{13}{25}$