Multiple Events: WJEC GCSE Higher June 2023 Unit 1 Q15

Higher June 2023 Unit 1 Q15

WJECHigherCurrent spec6 marksMultiple Events

15. A box contains 5 blue discs and 3 yellow discs.
Three discs are to be chosen at random, without replacement.

(a) Calculate the probability that the three discs chosen will all be the same colour. [3]

(b) Calculate the probability that exactly one blue disc is selected. [3]

Mark scheme (a)

Scheme	Marks	Comments
P(BBB or YYY) = \(\frac{5}{8} \times \frac{4}{7} \times \frac{3}{6} + \frac{3}{8} \times \frac{2}{7} \times \frac{1}{6}\) or equivalent	M2	M1 for sight of one correct product. M0 for use of an incorrect total e.g. 9. Must show intention to add for second M mark.
\(\frac{66}{336}\) (= \(\frac{11}{56}\)) or equivalent	A1	ISW If no marks awarded, SC1 for an answer of \(\frac{152}{512}\) or equivalent (from a method ‘with replacement’).

Mark scheme (b)

Scheme	Marks	Comments
P(BYY or YBY or YYB) \(\frac{5}{8} \times \frac{3}{7} \times \frac{2}{6} + \frac{3}{8} \times \frac{5}{7} \times \frac{2}{6} + \frac{3}{8} \times \frac{2}{7} \times \frac{5}{6}\) or \(\frac{5}{8} \times \frac{3}{7} \times \frac{2}{6} \times 3\) or equivalent	S1 M1	FT from part (a) consistent use of a wrongly calculated denominator (8 × 7 × 6) OR use of an incorrect total e.g. 9. Consideration of 3 permutations (may be implied) M1 implies S1. Must show intention to add for second mark.
\(\frac{90}{336}\) (= \(\frac{15}{56}\)) or equivalent	A1	ISW If no marks awarded, SC1 for sight of one correct product or SC1 for an answer of \(\frac{135}{512}\) or equivalent (from a method ‘with replacement’.

Scheme	Marks	Comments
1 – P(YYY or YBB or BYB or BBY or BBB)	S1
= 1 – [ \(\frac{3}{8} \times \frac{2}{7} \times \frac{1}{6} + \frac{3}{8} \times \frac{5}{7} \times \frac{4}{6} \times 3 + \frac{5}{8} \times \frac{4}{7} \times \frac{3}{6}\) ] or equivalent = 1 – [ \(\frac{6}{336} + \frac{180}{336} + \frac{60}{336}\) ]	M1	A complete method. FT ‘their P(BBB)’ or ‘their P(YYY)’ or both from (a). M1 implies S1.
\(\frac{90}{336}\) (= \(\frac{15}{56}\)) or equivalent	A1	ISW If no marks awarded, SC1 for 1 – [ \(\frac{3}{8} \times \frac{2}{7} \times \frac{1}{6} + \frac{3}{8} \times \frac{5}{7} \times \frac{4}{6} + \frac{5}{8} \times \frac{4}{7} \times \frac{3}{6}\) ] (= \(\frac{5}{8}\) ) from not considering 3 different permutations of BBY or SC1 for an answer of \(\frac{135}{512}\) or equivalent (from a method ‘with replacement’.