November 2025 (9709/52). Question 4

Gio has a pack of 18 cards. Ivy has a pack of x cards.

Each card has a picture of a bus or a car or a train. The number of cards with each picture in the two packs is shown in the table.

	Bus	Car	Train
Gio’s pack	6	10	2
Ivy’s pack	x – 12	9	3

One card is chosen at random from each pack. The probability that the two cards have pictures of buses on them is equal to twice the probability that the two cards have pictures of cars on them.

(a) Write down an equation in terms of x and hence find the value of x. [4 marks]

(b) Find the probability that the two cards have pictures of the same type of vehicle on them. [3 marks]

9709/52/M/J/25q3 – Mark Scheme

A bag contains 4 blue marbles and 12 red marbles. One marble is selected at random from the bag. If this marble is blue, it is replaced in the bag, but if it is red, it is not replaced. A second marble is now selected at random from the bag.

(a) Find the probability that both marbles selected are the same colour. [2 marks]

(b) Find the probability that the first marble is blue given that the second marble is red. [3 marks]

9709/53/M/J/25q5 – Mark Scheme

Bag A contains 6 red marbles, 5 blue marbles and 1 green marble.

Bag B contains 5 red marbles and 3 blue marbles.

A marble is chosen at random from bag A and placed in bag B.

A marble is now chosen at random from bag B.

(a) Draw a tree diagram to represent this information, giving the probability on each branch. [3 marks]

(b) Find the probability that both marbles chosen are the same colour. [2 marks]

(c) Find the probability that the marble chosen from bag A is blue, given that the marble chosen from bag B is blue. [3 marks]