I am sorry I don't know how to create in here so I have attached the picture of it, since this table contains the Data of the problem. So I have been asked to answer the following two questions.
$a)$Two students, one after another without replacement, were chosen randomly from the above sample of $600$ students. What is the probability that at least one of them have exceptional academic performance or both are from junior year of study?
$b)$Two students, one after another without replacement, were chosen randomly from the above sample of $600$ students. Given that at least one chosen student has exceptional academic performance, what is the probability that both chosen students are positive towards online lessons? Give your answer correct to $4$ decimal places.
MY WORKING
$a)$Now the cardinality of sample is given by: $|S|=\frac{600!}{598!*2!}=179700$
From table $|A|=85+45=130$
$|B|=85+290=375$
$|A\cap B|=85$
So: $P(AUB)$=$P(A)+P(B)-P(A\cap B)=0.0023$
$b)$Let $C$ be event that at least once chosen student has exceptional performance and $D$ be event that both chosen students have positive perception toward online classes then:
$|C|=85+45=130$
$|D|=64+29=93$
So $P(D/C)=\frac{P(C\cap D)}{P(C)}$
Now I don't know if I done both parts correctly. Kindly guide me and help me if I am making a mistake