A-LevelMathematicsProbability and statistics9709/62 · Oct/Nov 2018 · Q36 Marks
Jake attempts the crossword puzzle in his daily newspaper every day. The probability that he will complete the puzzle on any given day is 0.75, independently of all other days. Kenny also attempts the puzzle every day. The probability that he will complete the puzzle on a Monday is 0.8. The probability that he will complete it on a Tuesday is 0.9 if he completed it on the previous day and 0.6 if he did not complete it on the previous day.
- (i)Find the probability that he will complete the puzzle at least three times over a period of five days.[3]
- (ii)Find the probability that Kenny will complete the puzzle on at least one of the two days Monday and Tuesday in a randomly chosen week.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [M1] One binomial term ⁵Cₓpˣ(1 – p)⁵⁻ˣ, x ≠ 0 or 5, any p
- [M1] Correct unsimplified expression
- [A1] Correct final answer, allow 0.8965 (isw) but not 0.897 alone
- [B1] Unsimplified prob completed on no days
- [M1] 1 - 0.2 × a, a=0.1or 0.4 allow unsimplified
- [A1] Correct final answer
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