22M.1.SL.TZ1.10

pestleMathematicsAISLPaper 122M· sl-4-6-combined-mutually-exclusive-conditional-independence-prob-diagramssource ↗

Karl has three brown socks and four black socks in his drawer. He takes two socks at random from the drawer.

Complete the tree diagram.

[1]

Find the probability that Karl takes two socks of the same colour.

[2]

Given that Karl has two socks of the same colour find the probability that he has two brown socks.

[3]

Markscheme / solution

Note: Award A1 for both missing probabilities correct.

[1 mark]

multiplying along branches and then adding outcomes (M1)

$\frac{3}{7} \times \frac{2}{6} + \frac{4}{7} \times \frac{3}{6}$

$= \frac{18}{42} (= \frac{3}{7} \approx 0.429 (42.9 %))$ A1

[2 marks]

use of conditional probability formula M1

$\frac{(\frac{3}{7} \times \frac{2}{6})}{(\frac{3}{7})}$ A1

$= \frac{6}{18} (= \frac{1}{3}) (\frac{252}{756}, 0.333, 33.3 %)$ A1

[3 marks]

Examiners’ report

(a) It was pleasing to see that, for those candidates who made a reasonable attempt at the paper, many were able to identify the correct values on the tree diagram.

(b) Many identified at least one correct branch. Some who identified both correct branches and the respective probabilities failed to add their results.

Many identified at least one correct branch. Some who identified both correct branches and the respective probabilities failed to add their results.

Some candidates identified conditional probability evidenced by dividing a probability by their previous answer.