A-LevelMathematicsProbability and statistics9709/52 · May/June 2021 · Q15 Marks
An ordinary fair die is thrown repeatedly until a 5 is obtained. The number of throws taken is denoted by the random variable X.
- (a)Write down the mean of X.[1]
- (b)Find the probability that a 5 is first obtained after the 3rd throw but before the 8th throw.[2]
- (c)Find the probability that a 5 is first obtained in fewer than 10 throws.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- B1 WWW
- M1 p³(1-p) + p⁴(1 − p) + p⁵(1 −p) + p⁶(1 −p), 0 <p<1
- A1 At least 3s.f. Award at most accurate value.
- M1 p³-p⁷, 0<p<1
- A1 At least 3s.f. Award at most accurate value.
- M1 1-p⁹, 0< p < 1, n = 9, 10
- A1
- M1 p + p(1-p) + p(1 − p)² + p(1 −p)³ + p(1 −p)⁴ + p(1 − p)⁵ + p(1 –p)⁶ + p(1 − p)⁷ + p(1 –p)⁸ (+ p(1 − p)⁹), 0 <p< 1 As per answer for minimum terms shown
- A1
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