A-level · Probability

Calculating probabilities and sample spaceExam-style questions

Probability as the proportion of equally likely outcomes that are favourable; listing the sample space (including for two dice and two-way tables); the fact that probabilities of all outcomes sum to 1, and the complement rule P(A′) = 1 − P(A); and the difference between theoretical probability and experimental (relative frequency) probability.

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7 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4

1
A game is played using a bag containing $3$ $3$ red discs and $5$ $5$ white discs. In one turn, a player takes two discs at random from the bag, without replacement.
- If both discs are red, the player scores $1$ point.
- If exactly one disc is red, the player takes a third disc at random from the $6$ discs left in the bag, and scores $1$ point if this disc is red.
- Otherwise the player does not score.
At the end of each turn, all the discs are put back in the bag.
(a) Show that the probability that a player scores $1$ $1$ point in one turn is $\dfrac{2}{7}$ $\frac{2}{7}$ .

(2 marks)

Ravi and Sofia play the game.
(b) Ravi has three turns and Sofia has three turns. Find the probability that no points are scored in these six turns.

(1 mark)
(c) On another occasion, Ravi and Sofia have four turns each. Find the probability that Ravi's total score is exactly $3$ $3$ points more than Sofia's total score.

(3 marks)
Level 4 · 6 marksTry it