20N.1.SL.TZ0.T_6

pestleMathematicsAASLPaper 120N· sl-4-5-probability-concepts-expected-numberssource ↗

Srinivasa places the nine labelled balls shown below into a box.

Srinivasa then chooses two balls at random, one at a time, from the box. The first ball is not replaced before he chooses the second.

Find the probability that the first ball chosen is labelled $A$ .

[1]

a.i.

Find the probability that the first ball chosen is labelled $A$ or labelled $N$ .

[1]

a.ii.

Find the probability that the second ball chosen is labelled $A$ , given that the first ball chosen was labelled $N$ .

[2]

Find the probability that both balls chosen are labelled $N$ .

[2]

Markscheme / solution

$\frac{3}{9} (\frac{1}{3}, 0.333, 0.333333 \dots, 33.3 %)$ (A1) (C1)

[1 mark]

a.i.

$\frac{5}{9} (0.556, 0.555555 \dots, 55.6 %)$ (A1) (C1)

[1 mark]

a.ii.

$\frac{3}{8} (0.375, 37.5 %)$ (A1)(A1) (C2)

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

[2 marks]

$\frac{2}{9} \times \frac{1}{8}$ (M1)

Note: Award (M1) for a correct compound probability calculation seen.

$\frac{2}{72} (\frac{1}{36}, 0.0278, 0.0277777 \dots, 2.78 %)$ (A1) (C2)

[2 marks]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]