9709 P52 - Mar 2026 - Q4 - 9 marks
9024
Suri has a bag containing 4 blue discs and 3 yellow discs. She selects one disc at random, notes its colour and returns it to the bag. She repeats this process until she obtains a yellow disc.
(a) Find the probability that Suri obtains a yellow disc for the first time on her 4th selection. [1]
(b) Find the probability that Suri obtains a yellow disc for the second time on her 5th selection. [2]
Tan has a bag containing 4 red discs and 3 green discs. He selects discs at random, one at a time and without replacement, until he obtains a green disc. The random variable \(X\) is the number of discs he needs to select to obtain a green disc.
(c) Draw up the probability distribution table for \(X\). [3]
(d) Find \(\operatorname{Var}(X)\). [3]
