Higher November 2021 Paper 4 Q4

4 Li throws two fair four-sided dice, each numbered 1, 2, 3 and 4.
Li multiplies together the two numbers that the dice land on to produce a score.

Find the probability that Li’s score is a prime number. [4]

Mark scheme

Answer	Marks	Part marks and guidance
\(\dfrac{4}{16}\) oe nfww	4	M2 for 16 correct outcomes shown or for [4 × 4 =] 16 [outcomes] or M1 for table, list etc, with at least 10 correct outcomes to a maximum of 16 (ignoring repeats)	M marks are for products The outcomes may be a list or table showing 16 outcomes which may have numbers or ticks and crosses to show primes etc, if just numbers with nothing above 8 assume addition
		AND M2FT for correctly indicating all the primes in their outcomes (at least 6) and gives the correct response for their outcomes or M1FT for writing their correct response from their outcomes or for indicating all the primes in their outcomes with maximum one error to a maximum of 3 marks	By e.g. shading, underlining or ringing M1 implied by a correct numerator and a correct denominator for their list
		if 0 scored then SC3 for a correct response from adding 16 outcomes i.e. \(\frac{9}{16}\) or SC2 for a correct response from adding (at least 6 outcomes), primes must be indicated or SC1 for correct response from adding (at least 6 outcomes), primes are not indicated
		Note : an alternative method is M3 for [P(1 with 2,3 OR 2,3 with 1)=] \(\frac{1}{4} \times \frac{2}{4} + \frac{2}{4} \times \frac{1}{4}\) or M2 for the above method with one error or M1 for a correct tree diagram drawn	Note that \(\frac{2}{4} \times \frac{2}{4}\) is an incorrect method

e.g. (primes highlighted in bold)

1×1 2×1 3×1 4×1
1×2 2×2 3×2 4×2
1×3 2×3 3×3 4×3
1×4 2×4 3×4 4×4