A-LevelMathematicsProbability and statistics9709/52 · Oct/Nov 2021 · Q57 Marks
In a certain region, the probability that any given day in October is wet is 0.16, independently of other days.
- (a)Find the probability that, in a 10-day period in October, fewer than 3 days will be wet.[3]
- (b)Find the probability that the first wet day in October is 8 October.[2]
- (c)For 4 randomly chosen years, find the probability that in exactly 1 of these years the first wet day in October is 8 October.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [M1] One term: 10Cx p^x (1 – p)^(10–x) for 0 < x < 10, any p.
- [A1] Correct unsimplified expression, or better.
- [A1] 0.7935 < p < 0.794, mark at most accurate. If M0 scored, SC B1 for final answer 0.794.
- [M1] (1–p)^7 p, 0 < p < 1
- [A1] 0.0472144 to at least 3sf.
- [M1] 4C1 q^1 (1–q)^3, q = their (b) or correct.
- [A1] 0.163 < p < 0.1634, mark at most accurate from their probability to at least 3sf.
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