The probability that a teacher will give an unannounced test during any class is $\dfrac15$. If a student is absent twice then probability that he/she misses at least one test is
$\\ \hspace{5cm}$ a) $\dfrac23\ \quad $ b) $\dfrac45\ \quad$c) $\dfrac7{25}\ \quad $d) $\dfrac9{25}\ $
My attempt:
Probability of attending first test & missing $2$nd test $=\dfrac45\times\dfrac15=\dfrac4{25}$
Probability of missing first test & attending $2$nd test $=\dfrac15\times\dfrac45=\dfrac4{25}$
Probability of missing both the tests $=\dfrac15\times\dfrac15=\dfrac1{25}$
Total probability of missing at least one test $=\dfrac4{25}+\dfrac4{25}+\dfrac1{25}=\dfrac9{25}$
Can somebody please help me if I am wrong? Thanks.