1MA0 Higher June 2012 Paper 2 Q25
25 Carolyn has 20 biscuits in a tin.
She has 12 plain biscuits
5 chocolate biscuits
3 ginger biscuits
Carolyn takes at random two biscuits from the tin.
Work out the probability that the two biscuits were not the same type. (4)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(\frac{12}{20} \times \frac{11}{19} + \frac{5}{20} \times \frac{4}{19} + \frac{3}{20} \times \frac{2}{19}\) \(1 - \left(\frac{12}{20} \times \frac{11}{19} + \frac{5}{20} \times \frac{4}{19} + \frac{3}{20} \times \frac{2}{19}\right)\) | \(\dfrac{222}{380}\) | 4 | B1 for \(\frac{12}{19}\) or \(\frac{5}{19}\) or \(\frac{3}{19}\) (could be seen in working or on a tree diagram) M1 for \(\frac{12}{20} \times \frac{5}{19}\) or \(\frac{12}{20} \times \frac{3}{19}\) or \(\frac{5}{20} \times \frac{12}{19}\) or \(\frac{5}{20} \times \frac{3}{19}\) or \(\frac{3}{20} \times \frac{12}{19}\) or \(\frac{3}{20} \times \frac{5}{19}\) M1 for \(\frac{12}{20} \times \frac{5}{19} + \frac{12}{20} \times \frac{3}{19} + \frac{5}{20} \times \frac{12}{19} + \frac{5}{20} \times \frac{3}{19} + \frac{3}{20} \times \frac{12}{19} + \frac{3}{20} \times \frac{5}{19}\) A1 for \(\frac{222}{380}\) oe or 0.58(421...) OR B1 for \(\frac{8}{19}\) or \(\frac{15}{19}\) or \(\frac{17}{19}\) M1 for \(\frac{12}{20} \times \frac{8}{19}\) or \(\frac{5}{20} \times \frac{15}{19}\) or \(\frac{3}{20} \times \frac{17}{19}\) M1 for \(\frac{12}{20} \times \frac{8}{19} + \frac{5}{20} \times \frac{15}{19} + \frac{3}{20} \times \frac{17}{19}\) A1 for \(\frac{222}{380}\) oe or 0.58(421...) OR B1 for \(\frac{11}{19}\) or \(\frac{4}{19}\) or \(\frac{2}{19}\) M1 for \(\frac{12}{20} \times \frac{11}{19}\) or \(\frac{5}{20} \times \frac{4}{19}\) or \(\frac{3}{20} \times \frac{2}{19}\) M1 for \(1 - \left(\frac{12}{20} \times \frac{11}{19} + \frac{5}{20} \times \frac{4}{19} + \frac{3}{20} \times \frac{2}{19}\right)\) A1 for \(\frac{222}{380}\) oe or 0.58(421...) |
Notes
NB if decimals used they must be correct to at least 2 decimal places
SC : with replacementB2 for \(\frac{111}{200}\) oe
OR
e.g.
B0
M1 for \(\frac{12}{20} \times \frac{8}{20}\) or \(\frac{5}{20} \times \frac{15}{20}\) or \(\frac{3}{20} \times \frac{17}{20}\)
M1 for \(\frac{12}{20} \times \frac{8}{20} + \frac{5}{20} \times \frac{15}{20} + \frac{3}{20} \times \frac{17}{20}\)
A0