A-LevelMathematicsProbability and statistics9709/63 · Oct/Nov 2019 · Q710 Marks

A competition is taking place between two choirs, the Notes and the Classics. There is a large audience for the competition. * 30% of the audience are Notes supporters. * 45% of the audience are Classics supporters. * The rest of the audience are not supporters of either of these choirs. * No one in the audience supports both of these choirs.

(i)(a)A random sample of 6 people is chosen from the audience. Find the probability that no more than 2 of the 6 people are Notes supporters.[3]
(i)(b)Find the probability that none of the 6 people support either of these choirs.[2]
(ii)A random sample of 240 people is chosen from the audience. Use a suitable approximation to find the probability that fewer than 50 do not support either of the choirs.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[M1] Binomial term of form ⁶Cxpˣ(1-p)⁶⁻ˣ 0<p<1 any p, x ≠ 6,0
[A1] Correct unsimplified answer
[A1] Correct final answer
[M1] 0.25^n seen alone, 1 < n ≤6
[A1] Correct final answer
[B1FT] Correct unsimplified 240p and 240pq where p =their P(support neither choir) or 0.25
[M1] Substituting their μ and σ (condone σ²) into the ±Standardisation Formula with a numerical value for '49.5'.
[M1] Using continuity correction 49.5 or 50.5 within a standardisation expression
[M1] Appropriate area Φ from standardisation formula P(z<...) in final solution, (< 0.5 if z is –ve, > 0.5 if z is +ve)
[A1] Correct final answer

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