(a) Frances has three cards: Ace (A), King (K) and Queen (Q). She shuffles these cards and deals them one at a time.
(i) List all the different orders in which she can deal the cards. One possible order is already shown in the table. You may not need to use all the rows.
First card
Second card
Third card
A
K
Q
[2]
(ii) Find the probability that, in the three cards Frances deals, the King (K) is dealt immediately after the Queen (Q). [1]
(b) A counter has 3 on one side and 5 on the other. Lena flips the counter. She then picks one of these three cards at random.
Lena puts the card next to the counter and works out the answer.
Find the probability that Lena gets an answer less than 8. You must show your working. [4]
Mark scheme (a)
Answer
Marks
Part marks and guidance
(i) [A K Q] A Q K K A Q K Q A Q A K Q K A
2
B1 for 4 or 5 correct with repeats and/or errors or B1 for 2 or 3 correct with no repeats and/or errors
(ii) \(\dfrac{\textit{their}\ 2}{\textit{their}\ 6}\) oe isw
1FT
Strict FT dep on at least 4 correct orders seen in (i)
Must be their total QK ÷ their total orders Ignore attempts to cancel or convert to decimal/percentage Accept [0].33[3...] or 33[.3...]% or their correct decimal to 2sf Do not accept ratios
Mark scheme (b)
Answer
Marks
Part marks and guidance
\(\dfrac{4}{6}\) oe with supporting evidence
4
Mark from one method only
B3 for 5 more correct outcomes only or B2 for 4 more correct outcomes and up to one error or omission or B1 for 3 more correct outcomes and up to two errors or omissions
OR
B2 for [\(2 \times 3\) =] 6 outcomes B1 for [two above 8] 10 and 9 or [four below] 2, 4, 6, 7 If 0 scored SC1 for \(\dfrac{4}{6}\) without working or \(\dfrac{\textit{their}\ 4}{\textit{their}\ 6}\) from some working
Do not accept ratios Accept \(\dfrac{2}{3}\), 0.66 to 0.67, 66% to 67% Mark fraction and ignore attempt to change form or cancel
A complete list of outcomes is 3 – 1 = 2 or 2 3 \(\times\) 2 = 6 or 6 3 + 4 = 7 or 7 5 – 1 = 4 or 4 5 \(\times\) 2 or 10 Given in text 5 + 4 = 9 or 9
Accept 5 \(\times\) 2 and 5 + 4 etc
Their 4 from partial list, their 6 from partial list or stated total outcomes
