Because probability is a tricksy hobbit. The probability of being male or buying a green car is in fact NOT independent in this case. You are thinking (like I did) of random people walking in being male or female.. then randomly buyng a car. If I stated the problem as this: The odds of someone walking in and buying one of these 3 colors is this: P(g), P(r), P(b). Then i said the odds of a person's gender are this: P(m), P(f). We would indeed have 2 independent events, and we could calculate all the odds like you said. In fact given those probabilities up front, we could say how far off are actual data is from the expected return. And in fact the expected ratio of male to female buyers in each color should be EXACTLY the same in that case. Specifically the ratio of P(m) to P(f).

However, we are given ZERO probabilities. Instead we are given a set of data, and asked to fill in probabilities from that. Since the ratio of male to female is in no way the same for any of the 3 data points (red,blue and green). We have to make up probabilities for each. So in this case since we are working backwards from established data, the 2 events are very dependent on each other. If they are buying a green car P(m) and P(f) are very different than if they were buying a red car. The very definition of dependent. This problem was odd because it was "backward" from most problems. Instead of finding the odds of Events happening, we instead got a set of data points that said these events DID happen. Please find some P(x) that makes this data point the expected value.

Another confusing thing is you (and Me too trying to fit in with what you were doing) was trying to use the actual probability rules. Which work as long as we agree that what I said above is true and used my modified %. Plato cut right to the chase and realized immediately all this is doing is asking you to read a chart to find the P(x) to that makes the expected value in the chart. For example the

, We should just read the chart and say 18+48/120 = 11/20. No need to go the long way around

Hopefully I am explaining it clearly enough that you can follow that. If not let me know and I'll try to come up with another line of attack.