Answer:
(a) 0.7
(b) 
Step-by-step explanation:
Let
and
be the events of passing the 1st, 2nd, and 3rd exam individually.
Given that 
where
denotes the probability of passing the 1st exam.
Condition for passing the second exam is, at first, the candidate must have to pass the 1st exam.
So, 
where
denotes the probability of passing the 2nd exam when she already passed the 1st exam (given, 0.8).
Similarly, as the conditional probability of passing the 3rd exam is 0.7, and the condition for this is, at first, she must have to pass the 1st and 2nd exam. i.e,

(a) For passing all the exams, the condition is, at first, she has to pass the 1st and 2nd exam, then she has to pass the 3rd exam too. The probability for this conditional has been given as 0.7.
So, the probability that she passes all three exams is 0.7.
(b) Given that she didn't pass all three exams that means she either failed in 1st exam or she passed the 1st and failed in 2nd exam or she passed both 1st and 2nd but failed in the 3rd exam.
Let F be the event that she didn't pass all three exams. So,


Lef
be the event that she failed the 2nd exam, so


So, the conditional probability that she failed the 2nd exam is

