A-LevelMathematicsProbability and statistics9709/51 · Oct/Nov 2020 · Q35 Marks
Kayla is competing in a throwing event. A throw is counted as a success if the distance achieved is greater than 30 metres. The probability that Kayla will achieve a success on any throw is 0.25.
- (a)Find the probability that Kayla takes more than 6 throws to achieve a success.[2]
- (b)Find the probability that, for a random sample of 10 throws, Kayla achieves at least 3 successes.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [M1] (1-p)ⁿ, n = 6,7 0<p<1 (i.e. 0.75⁶ or 0.75⁷)
- [A1] 0.178, 729/4096
- [M1] Binomial term of form ¹⁰Cx pˣ (1-p)¹⁰⁻ˣ, 0<p<1, any p, x ≠ 0, 10
- [A1] Correct unsimplified expression for 1 – P(X≤2): 1 – (0.75¹⁰ + ¹⁰C₁ 0.25¹ 0.75⁹ + ¹⁰C₂ 0.25² 0.75⁸)
- [A1] 0.474 (accept 0.474 < p < 0.4744)
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