November 2025 (9709/52). Question 1

A coin is biased so that the probability of obtaining a head when it is thrown is 0.4. The coin is thrown repeatedly until the first head is obtained.

(a) Find the probability that the first head is obtained on the 5th throw. [1 mark]

(b) Find the probability that the first head is obtained after the 6th throw. [2 marks]

9709/52/M/J/25q4 – Mark Scheme

Vehicles approaching a certain road junction from Bromley must go either left, right or straight on. Over time, it is known that 30% turn left, 25% turn right and 45% go straight on. The driver of each vehicle chooses a direction independently of all other drivers.

(a) Find the probability that the next three vehicles approaching this junction from Bromley all go in different directions. [2 marks]

(b) Find the probability that, from the vehicles approaching this junction from Bromley today, the 1st vehicle to go left is before the 9th vehicle. [2 marks]

(c) Find the probability that, from the vehicles approaching this junction from Bromley today, the 2nd vehicle to go left is the 7th vehicle. [2 marks]

9709/53/M/J/25q2 – Mark Scheme

At a large college, all students who study Science also study exactly one of Art or Drama or Music. 20% of these students study Art, 45% study Drama and 35% study Music.

(a) 3 students are selected at random from the students who study Science.

Find the probability that at least 1 of these students studies Drama. [2 marks]

(b) 10 students are selected at random from the students who study Science.

Find the probability that more than 7 study Art or Music. [3 marks]

9709/53/M/J/25q3 – Mark Scheme

A fair six-sided dice with faces labelled 1, 2, 3, 4, 5, 6 is thrown repeatedly until a 3 is obtained. The number of throws taken is denoted by the random variable X.

(a) Find P(X=8) [1 mark]

(b) Find P(X<9) [2 marks]

(c) Find the probability that 3 is obtained for the second time before the 6th row. [3 marks]