Question

In a class of 125 students, 70 passed in English, 55 in mathematics and 30 in both. Find the probability that a student selected at random from the class has passed in at least one subject.

• A. $\frac{19}{25}$
• B. $\frac{6}{25}$
• C. $\frac{17}{25}$
• D. $\frac{8}{25}$

Answer 1

The correct option is A $\frac{19}{25}$

In a class of $125$ students, $70$ passed in English, $55$ passed in mathematics and $30$ passed in both.

$\Rightarrow n\left(\mu \right)=125,n\left(E\right)=70,n\left(M\right)=55,n(E\cap M)=30$

Total no.of students passed $=n(E\cup M)=n\left(E\right)+n\left(M\right)-n(M\cap E)=70+55-30=95$

$\therefore$ The total no.of students failed $=n\left(U\right)-n(E\cup M)=125-95=30$

The probability that student passed in atleast one subject $=\frac{n(E\cup M)}{n\left(U\right)}$

$=\frac{95}{125}=\frac{19}{25}$