Foundation November 2018 Paper 1 Q21
21 Here are five number cards.
\[\boxed{17} \quad \boxed{12} \quad \boxed{23} \quad \boxed{15} \quad \boxed{16}\]Two of the five cards are picked at random.
Work out the probability that the total of the two numbers is more than 30 [3 marks]
| Answer | Mark | Comments | ||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Alternative Method 1 | ||||||||||||||||||||||||||||||||||||||
| Lists at least 5 correct combinations or at least 5 correct outcomes or constructs correct two-way table eg 17 and 12 or 29 17 and 23 or 40 17 and 15 or 32 17 and 16 or 33 12 and 23 or 35 12 and 15 or 27 12 and 16 or 28 23 and 15 or 38 23 and 16 or 39 15 and 16 or 31 or
| M1 | outcomes may be seen in the two-way table ignore additional combinations such as 17 and 17 for M1 ignore any totals in a correctly constructed two-way table 17 and 12 & 12 and 17 are accepted as two different combinations | ||||||||||||||||||||||||||||||||||||
| Fully correct list or two-way table eg 29, 40, 32, 33, 35, 27, 28, 38, 39, 31 or 40, 32, 33, 35, 38, 39, 31 or
| A1 | accept ticks/crosses with correct pairs instead of values in the two-way table, it is acceptable to have only one set of ten cells completed (top right or bottom left) if all correct accept ticks and/or crosses in cells do not accept incorrect combinations such as 17 and 17 for A1 | ||||||||||||||||||||||||||||||||||||
| \(\dfrac{7}{10}\) or 0.7 or 70% | A1ft | oe ft their list or two-way table with M1 scored and a probability > 0 and < 1 | ||||||||||||||||||||||||||||||||||||
| Alternative Method 2 | ||||||||||||||||||||||||||||||||||||||
| States that outcomes of 30 or under may only be achieved by using the 12 | M1 | oe | ||||||||||||||||||||||||||||||||||||
| Lists the three (or six) combinations which give outcomes of 30 or under 12 and 15 (15 and 12) 12 and 16 (16 and 12) 12 and 17 (17 and 12) or Lists the three outcomes of 30 or under (may be repeated) 27 28 29 | A1 | |||||||||||||||||||||||||||||||||||||
| \(\dfrac{7}{10}\) or 0.7 or 70% | A1ft | oe ft their list with M1 scored and a probability > 0 and < 1 eg if only 27 and 28 found and answer 0.8 given score M1A0A1ft | ||||||||||||||||||||||||||||||||||||
Additional guidance
| Correct answer with no incorrect working | M1A1A1 | ||||||||||||||||||||||||||||||||||||
| If work is crossed out, this may be the removal of totals not above 30 and these should still be considered if appropriate | |||||||||||||||||||||||||||||||||||||
This example shows that the answer 0.7 may not score full marks.
and answer of 0.7 | M1A0A1ft | ||||||||||||||||||||||||||||||||||||
This is an example of following through from their table to give A1ft.
and answer of 0.6 | M1A0A1ft | ||||||||||||||||||||||||||||||||||||
| Ignore use of probability words unless contradictory |