November 2025 (9709/52). Question 2

Kayla has a bag containing 3 red marbles, 1 blue marble and 2 green marbles. She selects one marble from the bag at random and does not replace it in the bag. She repeats this process until she obtains a green marble. The random variable X is the number of marbles that she needs to select until she obtains a green marble.

(a) Draw up the probability distribution table for X. [4 marks]

(b) Find Var(X) [3 marks]

9709/51/M/J/25q6 – Mark Scheme

A bag contains 10 marbles, of which 4 are red and 6 are blue. Four marbles are selected from the bag at random, without replacement. The random variable X denotes the number of blue marbles selected.

(a) Show that P(X=2) = 3/7 [2 marks]

(b) Draw up the probability distribution table for X. [4 marks]

(c) Find the probability that at least 2 of the marbles chosen are blue, given that at least 1 red marble and at least 1 blue marble are chosen. [3 marks]

9709/52/M/J/25q1 – Mark Scheme

Rachel has three coins. The first coin is biased so that the probability of obtaining a head when it is thrown is 1/3. The second coin is biased so that the probability of obtaining a head when it is thrown is 1/4. The third coin is fair.

Rachel throws the three coins at the same time. The random variable X is the number of tails that she obtains.

Draw up the probability distribution table for X. [3 marks]