(b) Work out the probability that both dice land on a number less than 3 [1 mark]
(c) Work out the probability that exactly one of the dice lands on a number less than 3 [2 marks]
Mark scheme (a)
Answer
Mark
Comments
\(\dfrac{1}{3}\) or \(\dfrac{2}{6}\) or 0.33… or 33.(…)% on each top branch and \(\dfrac{2}{3}\) or \(\dfrac{4}{6}\) or 0.66… or 0.67 or 66.(…)% or 67% on each bottom branch
B1
accept any equivalent fraction, decimal or percentage
Additional guidance
Decimals must have at least 2 decimal places so do not accept 0.3 or 0.6 or 0.7
Only accept the percentages shown, do not accept 30% or 60%
Ignore working around the edge of the diagram
B1
Mark scheme (b)
Answer
Mark
Comments
\(\dfrac{1}{9}\) or 0.11… or 11.(…)%
B1
Additional guidance
Ignore probability words such as ‘unlikely’ or ‘evens’
oe accept 0.33… for \(\dfrac{1}{3}\) accept 0.66… or 0.67 for \(\dfrac{2}{3}\)
\(\dfrac{4}{9}\) or 0.44… or 44.(…)%
A1
Alternative method 3 Probabilities on branches in (a) not all correct
\(\dfrac{1}{3} \times\) their \(\dfrac{2}{3}\) where their \(\dfrac{2}{3}\) must be for 2nd dice 3 or more or their \(\dfrac{2}{3} \times\) their \(\dfrac{1}{3}\) where their \(\dfrac{2}{3}\) must be for 1st dice 3 or more and their \(\dfrac{1}{3}\) must be for 2nd dice less than 3
M1
oe accept 0.33… for \(\dfrac{1}{3}\) accept 0.66… or 0.67 for \(\dfrac{2}{3}\) their fractions must be between 0 and 1
\(\dfrac{4}{9}\) or 0.44… or 44.(…)%
A1ft
ft their fractions
Alternative method 4 Probabilities on branches in (a) not all correct
\(1 - \left(\dfrac{1}{3} \times \dfrac{1}{3}\right) - \left(\text{their } \dfrac{2}{3} \times \text{their } \dfrac{2}{3}\right)\) where their \(\dfrac{2}{3}\) must be for 1st dice 3 or more and their \(\dfrac{2}{3}\) must be for 2nd dice 3 or more
M1
accept 0.33… for \(\dfrac{1}{3}\) accept 0.66… or 0.67 for \(\dfrac{2}{3}\) their fractions must be between 0 and 1
\(\dfrac{4}{9}\) or 0.44… or 44.(…)%
A1ft
ft their fractions
Additional guidance
If probabilities on branches in (a) are all \(\dfrac{1}{3}\)
M0A0
Decimals must have at least 2 decimal places so do not accept 0.3 or 0.6 or 0.7
Ignore any incorrect cancelling or change of form (fraction, decimal or percentage)
