Question

The probability that a teacher will give an unannounced test during any class meeting is $\frac{1}{5}$. If a student is absent twice, then the probability that the student will miss atleast one test is

• A. $\frac{4}{5}$
• B. $\frac{7}{25}$
• C. $\frac{1}{5}$
• D. $\frac{9}{25}$

Answer 1

The correct option is D $\frac{9}{25}$

$P\text{(one test held)}=\frac{1}{5}\cdot \frac{4}{5}+\frac{4}{5}\cdot \frac{1}{5}=\frac{8}{25}$

$P\text{(test on both days)}=\frac{1}{5}\cdot \frac{1}{5}=\frac{1}{25}$

Required probability $=\frac{8}{25}+\frac{1}{25}=\frac{9}{25}$