2024 CJC H1 Q10

A box contains 5 blue balls, 2 green balls and 2 red balls. Two balls are selected at random, without replacement, from the box.

1. Draw a fully labelled tree diagram to represent all the possible outcomes[2]
2. Find the probability that the two balls are of the same colour.[2]
3. Find the probability that the first ball selected is blue, given that the two balls selected are of different colours.[3]
4. Determine whether the event 'first ball selected is blue' and the event 'two balls selected are of different colours' are independent, justifying your answer.[2]