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

$\frac{13}{25}$

Explanation for the correct option:

Finding the probability:

Given that, the total number of students in class is $125$.

The probability that the students passed Maths, $\mathrm{P}\left(\mathrm{M}\right)=\frac{70}{125}$

The probability that the students passed Statistics, $\mathrm{P}\left(\mathrm{S}\right)=\frac{55}{125}$

The probability that the students passed in both Mathematics and Statistics, $\mathrm{P}(\mathrm{M}\cap \mathrm{S})=\frac{30}{125}$

Now, the probability that a random student selected from the class has passed only one subject is given by,

$\mathrm{P}(\mathrm{M}\cap {\mathrm{S}}^{\text{'}})+\mathrm{P}({\mathrm{M}}^{\text{'}}\cap \mathrm{S})=\mathrm{P}\left(\mathrm{M}\right)+\mathrm{P}\left(\mathrm{S}\right)–2\mathrm{P}(\mathrm{M}\cap \mathrm{S})$

Substituting the required values from the above data we get,

$\begin{array}{rcl}\mathrm{P}\left(\mathrm{M}\cap {\mathrm{S}}^{\text{'}}\right)+\mathrm{P}\left({\mathrm{M}}^{\text{'}}\cap \mathrm{S}\right)& =& \frac{70}{125}+\frac{55}{125}–2\left(\frac{30}{125}\right)\\ & =& \left(\frac{70+55-60}{125}\right)\\ & =& \frac{65}{125}\\ & =& \frac{13}{25}\end{array}$

Hence, the correct option is A.