Higher June 2024 Paper 1 Q13

EdexcelHigherCurrent spec5 marksTree Diagrams

13 Harman has two bags of beads.

In bag A, there are 3 white beads and 7 black beads.
In bag B, there are 5 white beads and 4 black beads.

Harman takes at random a bead from bag A and a bead from bag B

(a) Complete the probability tree diagram.

Probability tree diagram with blank branch labels: bag A white or black, then bag B white or black on each branch

(2)

(b) Work out the probability that Harman takes two beads of the same colour. (3)

Mark scheme (a)

Scheme	Marks
\(\dfrac{3}{10}, \dfrac{7}{10}\) \(\dfrac{5}{9}, \dfrac{4}{9}\) \(\dfrac{5}{9}, \dfrac{4}{9}\)	B2
	(2)

Notes

B2: for all 3 correct pairs of probabilities on the correct branches

If not B2 then award B1 for 1 correct pair of probabilities on a correct branch

Allow equivalent fractions/decimals (to 2 dp truncated or rounded ie 0.55(…) and/or 0.44(…))

Mark scheme (b)

Scheme	Marks
\(\text{``}{\dfrac{3}{10}}\text{''} \times \text{``}{\dfrac{5}{9}}\text{''}\) oe or \(\text{``}{\dfrac{7}{10}}\text{''} \times \text{``}{\dfrac{4}{9}}\text{''}\) oe or \(\text{``}{\dfrac{3}{10}}\text{''} \times \text{``}{\dfrac{4}{9}}\text{''}\) oe or \(\text{``}{\dfrac{7}{10}}\text{''} \times \text{``}{\dfrac{5}{9}}\text{''}\) oe or	M1ft
\(\text{``}{\dfrac{3}{10}}\text{''} \times \text{``}{\dfrac{5}{9}}\text{''} + \text{``}{\dfrac{7}{10}}\text{''} \times \text{``}{\dfrac{4}{9}}\text{''}\) oe or \(1 - \left(\text{``}{\dfrac{3}{10}}\text{''} \times \text{``}{\dfrac{4}{9}}\text{''} + \text{``}{\dfrac{7}{10}}\text{''} \times \text{``}{\dfrac{5}{9}}\text{''}\right)\) oe	M1 ft
Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: \(\dfrac{43}{90}\)	A1ft
	(3)
	(5 marks)

Notes

M1ft: (probabilities < 1)

Allow equivalent fractions/decimals (to 2 dp truncated or rounded ie 0.55(…) and/or 0.44(…))

M1 ft: Allow equivalent fractions/decimals (to 2 dp truncated or rounded ie 0.55(…) and/or 0.44(…))

A1ft: oe
0.47(77..) to 2 dp truncated or rounded or 47.(77)% to 2 sf truncated or rounded