15 A packet of 6 pens contains 4 red pens and 2 blue pens.
A pen is taken at random from the packet and is not replaced. A second pen is then taken at random from the packet.
(a) Complete the tree diagram. [2]
(b) Find the probability of taking two pens of the same colour. [3]
Mark scheme (a)
Answer
Marks
Part marks and guidance
\(\frac{3}{5}\) and \(\frac{2}{5}\) oe correct on top branch
1
\(\frac{4}{5}\) and \(\frac{1}{5}\) oe correct on second branch
1
Mark scheme (b)
Answer
Marks
Part marks and guidance
\(\frac{7}{15}\) oe or 0.466 to 0.467
3
M2FT for \(\left(\frac{4}{6} \times \frac{3}{5}\right) + \left(\frac{2}{6} \times \frac{1}{5}\right)\) oe or better
or
M1FT for \(\left(\frac{4}{6} \times \frac{3}{5}\right)\) oe or \(\left(\frac{2}{6} \times \frac{1}{5}\right)\) oe may be implied by \(\frac{12}{30}\) oe or by \(\frac{2}{30}\) oe
FT their probabilities from (a) Working may be seen next to diagram If answers to products seen, then + may be implied by final answer
