1MA0 Higher March 2013 Paper 1 Q24
24 There are three different types of sandwiches on a shelf.
There are 4 egg sandwiches,
5 cheese sandwiches
and 2 ham sandwiches.
Erin takes at random 2 of these sandwiches.
Work out the probability that she takes 2 different types of sandwiches. (5)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| EE + CC + HH | \(\dfrac{76}{110}\) | 5 | M1 for use of 10 as denominator for 2nd probability M1 for \(\frac{4}{11} \times \frac{3}{10}\) or \(\frac{5}{11} \times \frac{4}{10}\) or \(\frac{2}{11} \times \frac{1}{10}\) M1 for \(\frac{4}{11} \times \frac{3}{10} + \frac{5}{11} \times \frac{4}{10} + \frac{2}{11} \times \frac{1}{10}\) \(\left(= \frac{34}{110}\right)\) M1 (dep on previous M1) for \(1 -\) ‘\(\frac{34}{110}\)’ A1 for \(\frac{76}{110}\) oe |
| Or EC+EH+CE+CH+HE+HC | Or M1 for use of 10 as denominator for 2nd probability M1 for \(\frac{4}{11} \times \frac{5}{10}\) or \(\frac{4}{11} \times \frac{2}{10}\) or \(\frac{5}{11} \times \frac{4}{10}\) or \(\frac{5}{11} \times \frac{2}{10}\) or \(\frac{2}{11} \times \frac{4}{10}\) or \(\frac{2}{11} \times \frac{5}{10}\) M2 for \(\frac{4}{11} \times \frac{5}{10} + \frac{4}{11} \times \frac{2}{10} + \frac{5}{11} \times \frac{4}{10} + \frac{5}{11} \times \frac{2}{10} + \frac{2}{11} \times \frac{4}{10} + \frac{2}{11} \times \frac{5}{10}\) (M1 for at least 3 of these) A1 for \(\frac{76}{110}\) oe | ||
| Or E,not E + C,not C + H,not H | Or M1 for use of 10 as denominator for 2nd probability M1 for \(\frac{4}{11} \times \frac{7}{10}\) or \(\frac{5}{11} \times \frac{6}{10}\) or \(\frac{2}{11} \times \frac{9}{10}\) M2 for \(\frac{4}{11} \times \frac{7}{10} + \frac{5}{11} \times \frac{6}{10} + \frac{2}{11} \times \frac{9}{10}\) (M1 for two of these added) A1 for \(\frac{76}{110}\) oe |
Notes
SC: B2 for \(\frac{76}{121}\)
SC: B1 for \(\frac{4}{11} \times \frac{4}{11} + \frac{5}{11} \times \frac{5}{11} + \frac{2}{11} \times \frac{2}{11}\) \(\left(= \frac{45}{121}\right)\)
Or
\(\frac{4}{11} \times \frac{5}{11} + \frac{4}{11} \times \frac{2}{11} + \frac{5}{11} \times \frac{4}{11} + \frac{5}{11} \times \frac{2}{11} + \frac{2}{11} \times \frac{4}{11} + \frac{2}{11} \times \frac{5}{11}\)
Or
\(\frac{4}{11} \times \frac{7}{11} + \frac{5}{11} \times \frac{6}{11} + \frac{2}{11} \times \frac{9}{11}\)