21M.1.SL.TZ1.10

pestleMathematicsAISLPaper 121M· sl-4-7-discrete-random-variablessource ↗

A game is played where two unbiased dice are rolled and the score in the game is the greater of the two numbers shown. If the two numbers are the same, then the score in the game is the number shown on one of the dice. A diagram showing the possible outcomes is given below.

Let $T$ be the random variable “the score in a game”.

Find the probability that

Complete the table to show the probability distribution of $T$ .

[2]

a player scores at least $3$ in a game.

[1]

b.i.

a player scores $6$ , given that they scored at least $3$ .

[2]

b.ii.

Find the expected score of a game.

[2]

Markscheme / solution

Note: Award A1 if three to five probabilities are correct.

[2 marks]

$\frac{32}{36} (\frac{8}{9}, 0.888888 \dots, 88.9 %)$ (A1)

[1 mark]

b.i.

use of conditional probability (M1)

e.g. denominator of $32$ OR denominator of $0.888888 \dots$ , etc.

$\frac{11}{32} (0.34375, 34.4 %)$ A1

[2 marks]

b.ii.

$\frac{1 \times 1 + 3 \times 2 + 5 \times 3 + \dots + 11 \times 6}{36}$ (M1)

$= \frac{161}{36} (4 \frac{17}{36}, 4.47, 4.47222 \dots)$ A1

[2 marks]

Examiners’ report

[N/A]

b.i.

[N/A]

b.ii.

[N/A]