78% of people who pass section A also pass section B.
36% of people who fail section A also fail section B.
(a) Complete the tree diagram. [2 marks]
(b) 40% of people who fail at least one section take the test again.
5000 people take the test.
How many of these 5000 people are expected to take the test again? [4 marks]
Mark scheme (a)
Answer
Mark
Comments
0.85 (Pass) and 0.15 (Fail) for Section A
B1
oe fractions, decimals or percentages
0.22 (Fail) on top branch for Section B and 0.64 (Pass) and 0.36 (Fail) on bottom branches for Section B
B1
oe fractions, decimals or percentages
Mark scheme (b)
Answer
Mark
Comments
Alternative method 1
their \(0.85 \times\) their 0.78 or 0.663 or their \(0.85 \times\) their 0.22 or 0.187 or their \(0.15 \times\) their 0.64 or 0.096 or their \(0.15 \times\) their 0.36 or 0.054
M1
oe ft their tree diagram provided all probabilities are \(\gt 0\) and \(\lt 1\)
\(1 -\) their 0.663 or their \(0.187 +\) their \(0.096 +\) their 0.054 or their \(0.187 + 0.15\) or 0.337
M1dep
oe their 0.663, their 0.187, their 0.096 and their 0.054 must be from correct methods
their \(0.337 \times 0.4\) or 0.1348 or their \(0.337 \times 5000\) or 1685
M1dep
oe fraction, decimal or percentage dep on M2
674
A1ft
ft their tree diagram provided all probabilities are \(\gt 0\) and \(\lt 1\)
Alternative method 2
their \(0.85 \times\) their \(0.78 \times 5000\) or 3315 or their \(0.85 \times\) their \(0.22 \times 5000\) or 935 or their \(0.15 \times\) their \(0.64 \times 5000\) or 480 or their \(0.15 \times\) their \(0.36 \times 5000\) or 270 or their \(0.15 \times 5000\) or 750
M2
M1 their \(0.85 \times 5000\) or 4250
implied by 374
implied by 192
implied by 108
ft their tree diagram provided all probabilities are \(\gt 0\) and \(\lt 1\)
\(5000 -\) their 3315 or their \(935 +\) their \(480 +\) their 270 or their \(935 +\) their 750 or 1685 or 374 and 192 and 108
M1dep
dep on M2
674
A1ft
ft their tree diagram provided all probabilities are \(\gt 0\) and \(\lt 1\)
