A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2025 · Q19 Marks
The random variables X and Y have independent distributions X ~ Po(3) and Y ~ Po(2) respectively.
- (a)Find P(2 < X < 5).[2]
- (b)Find P(X+Y > 2).[3]
- (c)The total of 100 random values of X and 150 random values of Y is denoted by T. Use a suitable approximating distribution to find P(T < 560).[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- M1 Allow one end error. Allow incorrect λ.
- A1
- B1 SOI. Need to be stating or using Poisson.
- M1 Allow one end error and any λ.
- A1 Alternative combinations method. B1 for one correct product, M1 for correct structure (incl 1 - ...) and probs of full set of totals = 1 or probs of full set of totals = 2. A1 for 0.875.
- B1 SOI.
- M1 For standardising. Must have sqrt. Allow with no or incorrect continuity correction.
- M1 For correct area consistent with their working.
- A1
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →