Kai takes two of the cards at random without replacement and finds the positive difference between the two numbers.
(a) Complete the table to show all of the possible differences.
[2]
(b) Find the probability that Kai takes two cards with a difference that is an even number or a factor of 10. [2]
Mark scheme (a)
Answer
Marks
Part marks and guidance
2
B1 for 3 or 4 correct entries
For 2 marks, ignore entries in shaded squares if they are 0’s For B1 ignore shaded squares
Mark scheme (b)
Answer
Marks
Part marks and guidance
\(\frac{6}{12}\) oe nfww
2
If shaded squares are blank or all have zeros FTtheir 12 entries for 2 marks
M1 for all their even numbers and all factors of 10 identified only
IF Shaded SQUARES are counted: FTtheir 16 entries
B2FTtheir table Or M1 for all their even numbers and all factors of 10 identified only
If 0 scored SC1 for answer \(\dfrac{6}{16}\)
isw conversion/cancelling after their correct probability Do not accept ratio or words If table correct and shaded squares have zeros allow answer \(\frac{10}{16}\) oe for 2 marks
M1 may be seen on table by e.g. ringing values or listing
We only accept the 16 squares in the Grid, not the card values
Count zero as an even number
If table correct apart from all zeros in shaded squares allow all even numbers and factors of 10 [0’s in shaded squares] identified
For SC1 allow answer \(\dfrac{3}{8}\) if \(\dfrac{6}{16}\) seen first
