Multiple Events: WJEC GCSE Higher November 2019 Unit 2 Q14

Higher November 2019 Unit 2 Q14

WJECHigherCurrent spec5 marksMultiple Events

14. The following twelve cards are placed in a box.

CON

CLEM

SCARL

Three cards are chosen at random from the box at the same time.

(a) Calculate the probability that the three cards drawn are all the letter ‘C’. [2]

(b) The letters A, E and O are vowels. All the other letters on these cards are consonants.

Calculate the probability that the three cards drawn include at least one consonant and at least one vowel. [3]

Mark scheme (a)

Scheme	Marks	Comments
\(\frac{3}{12} \times \frac{2}{11} \times \frac{1}{10}\)	M1
\(= \tfrac{6}{1320}\ \left(= \tfrac{1}{220}\right)\) ISW	A1	Accept decimal answer of 0.0045(45…)

Mark scheme (b)

Scheme	Marks	Comments
(1−‘three vowels’−‘three consonants’) \(= 1 - \frac{3}{12} \times \frac{2}{11} \times \frac{1}{10} - \frac{9}{12} \times \frac{8}{11} \times \frac{7}{10}\)	M2	M1 for \(\tfrac{3}{12} \times \tfrac{2}{11} \times \tfrac{1}{10} + \tfrac{9}{12} \times \tfrac{8}{11} \times \tfrac{7}{10}\) OR \(1 - \tfrac{3}{12} \times \tfrac{2}{11} \times \tfrac{1}{10}\) OR \(1 - \tfrac{9}{12} \times \tfrac{8}{11} \times \tfrac{7}{10}\)
\(= \tfrac{810}{1320}\ \left(= \tfrac{27}{44}\right)\) ISW	A1	Accept decimal answer of 0.61(36…) If no marks award SC1 for an answer of \(\tfrac{972}{1728}\ \left(= \tfrac{36}{64}\ \text{or}\ \tfrac{9}{16}\right)\) ISW from working with replacement.

Scheme	Marks	Comments
P(Two vowels, one consonant ) + P(One vowel, two consonants = ) \(3 \times \tfrac{3}{12} \times \tfrac{2}{11} \times \tfrac{9}{10} + 3 \times \tfrac{3}{12} \times \tfrac{9}{11} \times \tfrac{8}{10}\) OR \(3 \times \tfrac{9}{12} \times \tfrac{3}{11}\ \left(\times \tfrac{10}{10}\right)\)	M2	M1 for \(3 \times \tfrac{3}{12} \times \tfrac{2}{11} \times \tfrac{9}{10}\) OR \(3 \times \tfrac{3}{12} \times \tfrac{9}{11} \times \tfrac{8}{10}\) OR \(\tfrac{3}{12} \times \tfrac{2}{11} \times \tfrac{9}{10} + \tfrac{3}{12} \times \tfrac{9}{11} \times \tfrac{8}{10}\) NB: sight of \(\tfrac{9}{12} \times \tfrac{3}{11} \times \tfrac{10}{10}\) gains M1, but \(\tfrac{9}{12} \times \tfrac{3}{11}\) gains M0.
\(= \tfrac{810}{1320}\ \left(= \tfrac{81}{132}\ or\ \tfrac{27}{44}\right)\) ISW	A1	Accept decimal answer of 0.61(36…) If no marks, award SC1 for an answer of \(\tfrac{972}{1728}\ \left(= \tfrac{36}{64}\ or\ \tfrac{9}{16}\right)\) ISW from working with replacement.