A-LevelMathematicsProbability and statistics9709/63 · Oct/Nov 2017 · Q36 Marks

At the end of a revision course in mathematics, students have to pass a test to gain a certificate. The probability of any student passing the test at the first attempt is 0.85. Those students who fail are allowed to retake the test once, and the probability of any student passing the retake test is 0.65.

(i)Draw a fully labelled tree diagram to show all the outcomes.[2]
(ii)Given that a student gains the certificate, find the probability that this student fails the test on the first attempt.[4]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[M1] Correct shape
[A1] All correct labels and probabilities
[M1] P(P) consistent with their tree diagram seen anywhere
[A1] Correct unsimplified P(P) seen as num or denom of a fraction
[M1] P(F∩P) found as correct product or consistent with their tree diagram seen as num or denom of a fraction
[A1] = 0.103 or 39/379

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