Question

The probability that a teacher will give a surprise test during any class meeting is $\frac{3}{5}$. If a student is absent on two days, then the probability that he will miss at least one test is

• A. $\frac{12}{25}$
• B. $\frac{9}{25}$
• C. $\frac{21}{25}$
• D. $\frac{4}{25}$

Answer 1

The correct option is C $\frac{21}{25}$

Possible cases are:
$\left(i\right)$ There were tests on both days:
$=\frac{3}{5}\times \frac{3}{5}=\frac{9}{25}$
$\left(ii\right)$ There was a test only on one of the days:
$={}^2{C}_1\times \frac{3}{5}\times (1-\frac{3}{5})=\frac{12}{25}$
Therefore, the required probability
$=\frac{9}{25}+\frac{12}{25}=\frac{21}{25}$