A-LevelMathematicsProbability and statistics9709/53 · May/June 2022 · Q47 Marks
Ramesh throws an ordinary fair 6-sided die.
- (a)Find the probability that he obtains a 4 for the first time on his 8th throw.[1]
- (b)Find the probability that it takes no more than 5 throws for Ramesh to obtain a 4.[2]
- (c)For 10 randomly chosen throws of the two dice, find the probability that Ramesh obtains a total of less than 4 on at least three throws.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [B1] (5/6)⁷ × (1/6) = 0.0465, 78125/1679616. 0.0465 < p < 0.04652
- [M1] 1-pⁿ, 0 < p < 1, n = 4, 5, 6 or sum of 4, 5 or 6 terms p×(1-p)ⁿ for n = 0,1,2,3,4(5).
- [A1] 0.598, 4651/7776
- [B1] [Probability of total less than 4 is] 3/36 or 1/12. SOI
- [M1] One term ¹⁰Cₓ pˣ (1−p)¹⁰⁻ˣ, for 0 < x < 10, 0 < p < 1.
- [A1 FT] Correct expression. Accept unsimplified.
- [A1] 0.0445. 0.04448 < p < 0.0445
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