In a room, there are 4 people who speak English and 5 people who speak French. If you randomly select two people from the room to have a conversation, what is the probability that they can communicate with each other in either English or French?
Let's break down this problem step-by-step:

1. There are a total of 9 people in the room.
2. We need to find the probability that both people selected speak English or both speak French.
3. The probability of selecting two English speakers is (4/9) * (3/8), since there are 4 English speakers out of 9 people initially, and then 3 out of the remaining 8 after one person is chosen.
4. Similarly, the probability of selecting two French speakers is (5/9) * (4/8).
5. To find the overall probability, we add these probabilities together: [(4/9) * (3/8)] + [(5/9) * (4/8)]

The final answer is 20/36, which simplifies to 5/9.