A-LevelMathematicsProbability and statistics9709/51 · Oct/Nov 2024 · Q14 Marks
Nicola throws an ordinary fair six-sided dice. The random variable X is the number of throws that she takes to obtain a 6.
- (a)Find P(X<8).[2]
- (b)Find the probability that Nicola obtains a 6 for the second time on her 8th throw.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.
- [M1] 1-b^d, b = 5/6, d=7, 8.
- [M1] 1 – c^e – (1 – c) × c^(e−1), c = 5/6, e = 8,9.
- [A1] 0.720918... 201811/279936
- [SC B1] If MO scored, SC B1 for 0.7209... or 201811/279936 only.
- [M1] (5/6)^6 × (1/6)^2 × 7 d an integer ≥ 1, no inappropriate addition.
- [A1] 0.0651 < p < 0.06512.
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