A-LevelMathematicsProbability and statistics9709/52 · May/June 2020 · Q79 Marks
On any given day, the probability that Moena messages her friend Pasha is 0.72.
- (a)Find the probability that for a random sample of 12 days Moena messages Pasha on no more than 9 days.[3]
- (b)Moena messages Pasha on 1 January. Find the probability that the next day on which she messages Pasha is 5 January.[1]
- (c)Use an approximation to find the probability that in any period of 100 days Moena messages Pasha on fewer than 64 days.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [M1] 1 - P(10, 11, 12)
- [M1] = 1 - [¹²C₁₀0.72¹⁰0.28² + ¹²C₁₁0.72¹¹0.28¹+0.72¹²]
- [A1] 1-(0.19372+0.09057+0.01941)
- [A1] 0.696
- [B1] 0.28³ × 0.72 = 0.0158
- [M1] Mean = 100 × 0.72 = 72
- [M1] Var = 100 × 0.72 × 0.28 = 20.16
- [M1] P(less than 64) = P(Z < (63.5 - 72)/√20.16)
- [M1] Using either 63.5 or 64.5 within a ±standardisation formula
- [M1] Appropriate area Φ, from standardisation formula P(z<...) in final solution = P(z<-1.893)
- [A1] 0.0292
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