A-LevelMathematicsProbability and statistics9709/53 · May/June 2022 · Q610 Marks

Sajid is practising for a long jump competition. He counts any jump that is longer than 6 m as a success. On any day, the probability that he has a success with his first jump is 0.2. For any subsequent jump, the probability of a success is 0.3 if the previous jump was a success and 0.1 otherwise. Sajid makes three jumps.

(a)Draw a tree diagram to illustrate this information, showing all the probabilities.[2]
(b)Find the probability that Sajid has exactly one success given that he has at least one success.[5]
(c)Find the probability that only his first three jumps are successes or only his last three jumps are successes.[3]

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 (May/June 2022). The mark or mark type is shown in brackets.

[B1] First and second jumps correct with probabilities and outcomes identified.
[B1] Third jump correct with probabilities and outcomes identified.
[M1] Two or three correct 3 factor probabilities added, correct or FT from part 6(a). Accept unsimplified.
[A1] Accept unsimplified.
[B1 FT] Accept unsimplified.
[M1] Accept unsimplified.
[A1] 0.7215 < p < 0.722
[M1] a×b×c×d×e×f FT from their tree diagram. Either a, b and c all = 0.8 or 0.9 (at least one of each) and d, e and f all = 0.1 or 0.3 (at least one of each). Or a, b, c = 0.2 or 0.3 (at least one of each) and d, e, f = 0.7 or 0.9 (at least one of each).
[A1] Either correct. Accept unsimplified.
[A1] [Total =] 0.0160[38]

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