A-LevelMathematicsProbability and statistics9709/52 · Oct/Nov 2020 · Q15 Marks
A fair six-sided die, with faces marked 1, 2, 3, 4, 5, 6, is thrown repeatedly until a 4 is obtained.
- (a)Find the probability that obtaining a 4 requires fewer than 6 throws.[2]
- (b)On another occasion, the die is thrown 10 times. Find the probability that a 4 is obtained at least 3 times.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [M1] 1 – p⁵, n = 5,6 or p + pq + pq² + pq³ + pq⁴ (+ pq⁵) 0 < p < 1, p + q = 1,
- [A1] AG, WWW
- [M1] ¹⁰Cx pˣ(1-p)¹⁰⁻ˣ, 0 < p < 1, any p, x ≠ 0,10
- [A1] Correct expression, accept unsimplified, condone omission of final bracket
- [A1] 0.2247<p ≤ 0·225, WWW
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