The table shows the number of each type of card in the bags.
Yes
No
Bag A
3
2
Bag B
1
9
In the game, a player picks one card at random from each bag.
The cards are then put back into the bags.
(a) Complete the tree diagram. [2 marks]
(b) To win a prize, a player must pick two cards marked Yes.
450 people each play the game once.
How many people are expected to win a prize? [3 marks]
Mark scheme (a)
Answer
Mark
Comments
Yes \(\dfrac{3}{5}\) and No \(\dfrac{2}{5}\) for Bag A
B1
oe fraction, decimal or percentage
Yes \(\dfrac{1}{10}\) and No \(\dfrac{9}{10}\) for both pairs of branches on Bag B
B1
oe fraction, decimal or percentage
Mark scheme (b)
Answer
Mark
Comments
their \(\dfrac{3}{5}\) \(\times\) their \(\dfrac{1}{10}\) or \(\dfrac{3}{50}\)
M1
oe may be on tree diagram ft their tree diagram if their \(\dfrac{3}{5}\) and their \(\dfrac{1}{10}\) are \(\gt 0\) and \(\lt 1\)
their \(\dfrac{3}{5}\) \(\times\) their \(\dfrac{1}{10}\) \(\times\) 450 or \(\dfrac{3}{50}\) \(\times\) 450
M1dep
oe their \(\dfrac{3}{50}\) must be \(\gt 0\) and \(\lt 1\)
27
A1ft
ft their tree diagram if their \(\dfrac{3}{5}\) and their \(\dfrac{1}{10}\) are \(\gt 0\) and \(\lt 1\)
Additional guidance
For the first mark, accept the correct probability shown on the tree diagram and ignore other probabilities
For the first mark, do not allow \(\dfrac{3}{5} \times \dfrac{1}{10}\) seen as part of a longer multiplication string of probabilities eg \(\dfrac{3}{5} \times \dfrac{1}{10} \times \dfrac{9}{10}\)
M0
Check tree diagram for working
\(\dfrac{27}{450}\) implies
M1M1A0
Students with incorrect probabilities on the tree diagram can score marks for follow through in part (b) or from the correct probabilities recovered eg probabilities of \(\dfrac{3}{4}\) and \(\dfrac{9}{10}\) on the top row of the tree diagram but an answer of 27 in part (b)
B0B0 in (a) M1M1A1 in (b)
Allow follow through from values rather than probabilities on the branches, with denominator 5 for Bag A and 10 for Bag B eg from 2 on Bag A and 9 on Bag B allow \(\dfrac{2}{5} \times \dfrac{9}{10} \times 450 = 162\)
M1M1A1ft
For A1ft allow a correct decimal answer or the answer truncated or rounded up to the nearest integer eg from \(\dfrac{3}{4}\) and \(\dfrac{1}{10}\) leading to \(\dfrac{3}{40} \times 450\) accept 33 or 33.75 or 34
