A-LevelMathematicsProbability and statistics9709/52 · Oct/Nov 2023 · Q15 Marks

A competitor in a throwing event has three attempts to throw a ball as far as possible. The random variable X denotes the number of throws that exceed 30 metres. The probability distribution table for X is shown below. x | 0 | 1 | 2 | 3 P(X = x) | 0.4 | p | r | 0.15

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

[M1] Using sum of probabilities = 1 to form an equation. Accept p + r = 0.45 oe.
[M1] Use E(X) = 1.1 to form an equation. Accept p + 2r = 0.65 oe. NB: These marks can be gained in either order; the second M may have an algebraic substitution.
[A1] p = 0.25, r = 0.2
[M1] Correct formula for variance method using their probability distribution table, 0 < their P(x) < 1.
[A1] = 1.19, 119/100. If M0 awarded, SC B1 for 1.19 www. 119/100 is A0.

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.

Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, Oct/Nov 2023 Paper 5 Variant 2, question 1.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content