Explanation:
out of the total possibilities of 20 student council members, 8 are in Nina's math class, and 6 are in Nina's science class.
as I understand the given information, out of these 14 council members, 4 are in her math and in her science class. but this is then irrelevant for the question (and do not add more possibilities), as these 4 are already covered by the 8 and 6 in her individual classes.
remember, a probability is always
desired cases / possible cases
so, let's pick the first random choice :
the probabilty to pick one that is either in her math or her science class is
14/20 = 7/10
because there are 20 total possibilities to pick from, and 14 of these 20 are in at least one of her classes.
now let's pick the second one.
I assume the first pick has not been returned to the pool and cannot be picked a second time.
so, this time we have therefore only 19 total choices, and 13 of them are in at least one of Nina's classes.
so, the probability for the second pick is
13/19
so, the probability that both picks are in at least one of her classes is then the combination of both probabilities (they have to happen together) :
7/10 × 13/19 = 91/190 = 0.478947368...