Here's the example.
I have 10 boxes consisting of 5 matching pairs of items (red gloves, red socks, blue socks, gold earrings, diamond earrings).
What are the odds of choosing two boxes with the same contents to complete a pair at each stage of the game?
Assuming the first two boxes are opened and they are matching red gloves, the odds would be...? Then the second two boxes are opened and they are matching diamond earrings, the odds are then...?
Presumably as each pair is opened and they match, the odds of matching the next two boxes become more likely as the variables decrease, but the odds that I managed to match them all in succession get less likely?
You don't require conditional probability to solve this.
You have 10 items hidden in boxes, consisting of 5 paired items.
There is no bias on selecting boxes in each stage.
The Total Space consists of $\Box$ ways to pick any boxes 2 at a time.
The Favored Space consists of $\Box$ ways to pick pairs each time.
The probability is therefore: $$\frac{\Box}{\Box}$$