S2 conditional probability

Given that there were exactly 6 reported first aid incidents in a 2 week period, find the probability that exactly 4 were reported in the first week.

I understand that this conditional probability question because of the 'given that' phrase at the start. But I don't understand why I have to do P=4 * P=2 divided by P*6

In a similar question (below), there was no 'given that' phrase so how would I know that I needed to divide by P=21 ?

In a randomly selected two-month period, 21 packages were lost. Find the probability that at least 10 packages were lost in each of these two months.

Conditional probability: $P(A|B) = P(A \& B)/P(B)$

In this case A is "4 in the first week" and B is "6 in 2 week period"

So P(A&B) means 4 in the first week and 6 overall, so it must be 4 in the first week and 2 in the second week. Otherwise you won't have 6 in the 2 week period. And given they're independent, we have P(4 in the fist week) * P(2 in the second week)



It's telling you 21 packages were lost, so it's restricting the situation from all possible situations. Then it says "in each of these two months", so you know it's refering to the same two month period, i.e. the one where there were 21 packages lost.

PS. You need to tighten up your notation: P=21 is gibberish, though I can interpret what you mean in this circumstance.