9709 P53 - Jun 2026 - Q4 - 9 marks
9180
Ebere has a biased coin with probability \(1/4\) of obtaining a head. She also has two bags containing coloured discs. Bag A contains 5 red discs and 3 blue discs. Bag B contains 4 red discs and 5 green discs.
Ebere tosses her coin. If she obtains a head, she chooses two discs from bag A, at random, one at a time and without replacement. If she obtains a tail, she chooses two discs from bag B in the same way.
(a) Draw a fully labelled tree diagram to represent this information. [2]
(b) Find the probability that Ebere obtains two discs of the same colour. [3]
(c) Find the probability that Ebere obtained a head with her coin given that at least one of the discs is red. [4]
