A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2017 · Q35 Marks
An experiment consists of throwing a biased die 30 times and noting the number of 4s obtained. This experiment was repeated many times and the average number of 4s obtained in 30 throws was found to be 6.21.
- (i)Estimate the probability of throwing a 4.[1]
- (ii)find the variance of the number of 4s obtained in 30 throws,[1]
- (iii)find the probability that in 15 throws the number of 4s obtained is 2 or more.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [1] (i) p = 0.207
- [1] (ii) Var = 30 × 0.207 × 0.793 = 4.92
- [1] (iii) P(> 2) = 1 - P(0, 1)
- [1] (iii) = 1 - (0.793)¹⁵ - (¹⁵C₁) (0.207)¹(0.793)¹⁴ seen n =15 p = any prob
- [1] (iii) = 0.848
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