I came across the following conditional probability questions. According to my comprehension, the question is asking only the probability concerning that yellow candy came from the old bag. However, some of my colleagues are arguing that we need to calculate the probability of both; yellow and green.
However, this is what I think the correct answer is, am I correct?:
As you are finding conditional probability, you need to first check the given condition. The given condition is that you have drawn one candie each from the old and the new bag and one of the candies is yellow and one of the candies is green. Now there are two possibilities - $i)$ the yellow candie came from the old bag and the green candie came from the new bag $ii)$ the yellow candie came from the new bag and the green candie came from the old bag.
As per the question, you need to find the conditional probability that the yellow candie came from the old bag (and that the green candie came from the new bag). So it should be,
$ \small P(\text {yellow from old bag}| \text{one green and one yellow}) = \dfrac{P(A)}{P(A) + P(B)}$
where,
$ \small P(A) = P(\text{yellow from old bag}) \cdot P(\text{ green from new bag})$
$ \small P(B) = P(\text{green from old bag}) \cdot P(\text{ yellow from new bag})$