19N.1.SL.TZ0.T_9

pestleMathematicsAISLPaper 119N· sl-4-5-probability-concepts-expected-numberssource ↗

Sungwon plays a game where she rolls a fair $6$ -sided die and spins a fair spinner with $4$ equal sectors. During each turn in the game, the die is rolled once and the spinner is spun once. The score for each turn is the sum of the two results. For example, $1$ on the die and $2$ on the spinner would receive a score of $3$ .

The following diagram represents the sample space.

Sungwon takes a second turn.

Find the probability that Sungwon’s score on her first turn is greater than $4$ .

[2]

Find the probability that Sungwon scores greater than $4$ on both of her first two turns.

[2]

Sungwon will play the game for $11$ turns.

Find the expected number of times the score on a turn is greater than $4$ .

[2]

Markscheme / solution

$\frac{18}{24} (\frac{3}{4}, 0.75, 75 %)$ (A1)(A1) (C2)

Note: Award (A1) for correct numerator, (A1) for correct denominator.

[2 marks]

$\frac{18}{24} \times \frac{18}{24}$ (M1)

Note: Award (M1) for the square of their probability in part (a).

$= 0.563 (\frac{9}{16}, \frac{324}{576}, 0.5625, 56.3 %)$ (A1)(ft) (C2)

Note: Follow through from part (a), provided their answer is less than or equal to $1$ .

[2 marks]

$11 \times \frac{18}{24}$ (M1)

Note: Award (M1) for multiplying their part (a) by $11$ .

$8.25 (\frac{33}{4})$ (A1)(ft) (C2)

Note: Follow through from part (a), provided their answer is less than or equal to $1$ .

[2 marks]

Examiners’ report

[N/A]