16 A fair spinner has five equal sections numbered 1, 2, 3, 4 and 5
A fair six-sided dice has five red faces and one green face.
The spinner is spun.
If the spinner shows an even number, the dice is thrown.
(a) Complete the tree diagram for the spinner and the dice. [2 marks]
(b) Work out the probability of getting an even number and the colour green. [2 marks]
Mark scheme (a)
Answer
Mark
Comments
\(\dfrac{2}{5}\) Even and \(\dfrac{3}{5}\) Odd
B1
oe fractions, decimals or percentages
Two branches from Even labelled Red \(\dfrac{5}{6}\) \(\qquad\) Green \(\dfrac{1}{6}\)
B1
oe fractions, decimals or percentages Branches from Odd is B0 Allow equivalent labelling eg R and G Green and Not Green
Additional guidance
In decimals, allow for \(\dfrac{5}{6}\) and \(\dfrac{1}{6}\) 0.83 and 0.17 or 0.833 and 0.167 or 0.834 and 0.166 or 0.84 and 0.16 or better truncation or rounding (sum of pair must equal 1) In percentages, allow for \(\dfrac{5}{6}\) and \(\dfrac{1}{6}\) 83% and 17% or 83.3% and 16.7% or 83.4% and 16.6% or 84% and 16% or better truncation or rounding (sum of pair must equal 100%)
Ignore any attempts to combine probabilities to the right of the tree diagram
Mark scheme (b)
Answer
Mark
Comments
their \(\dfrac{2}{5} \times\) their \(\dfrac{1}{6}\)
M1
their P(Even) \(\times\) their P(Green) ft from (a) if \(0 \lt\) both probabilities \(\lt 1\)
\(\dfrac{2}{30}\) or \(\dfrac{1}{15}\)
A1ft
oe fraction or decimal ft from (a) if \(0 \lt\) both probabilities \(\lt 1\)
Additional guidance
Allow 0.06 or 6% or better truncation or rounding or 0.07 or 7% for \(\dfrac{2}{30}\)
If the dice branches are not labelled there is no ft from (a)
If (a) has no attempt or an incorrect answer full marks can still be gained here for correct working (and answer)
Ignore further attempts to simplify or convert to a decimal or percentage after a correct fraction is seen eg \(\;\dfrac{2}{30} = \dfrac{1}{10}\) or \(\dfrac{4}{60} = 0.165\)
