A-LevelMathematicsProbability and statistics9709/52 · Feb/Mar 2020 · Q28 Marks

An ordinary fair die is thrown repeatedly until a 1 or a 6 is obtained.

(a)Find the probability that it takes at least 3 throws but no more than 5 throws to obtain a 1 or a 6.[3]
(b)On another occasion, this die is thrown 3 times. The random variable X is the number of times that a 1 or a 6 is obtained. Draw up the probability distribution table for X.[3]
(c)Find E(X).[2]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.

M1 One correct term with 0<p<1
A1 Correct expression, accept unsimplified
A1
B1 Probability distribution table with correct values of x, no additional values unless with probability of 0 stated, at least one non-zero probability included
B1 1 correct probability seen (may not be in table) or 3 or 4 non-zero probabilities summing to 1
B1 All probabilities correct
M1 Correct method from their probability distribution table with at least 3 terms, 0 ≤ their P(x) ≤ 1, accept unsimplified
A1

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source: A-Level Mathematics, Feb/Mar 2020 Paper 5 Variant 2, question 2.

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