A-LevelMathematicsProbability and statistics9709/62 · May/June 2019 · Q36 Marks

The probability that Janice will buy an item online in any week is 0.35. Janice does not buy more than one item online in any week.

(i)Find the probability that, in a 10-week period, Janice buys at most 7 items online.[3]
(ii)The probability that Janice buys at least one item online in a period of n weeks is greater than 0.99. Find the smallest possible value of n.[3]

Mark scheme

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

[M1] Binomial term of form ¹⁰Cₓpˣ(1 –p)¹⁰⁻ˣ 0<p<1 any p, x ≠ 10,0 (for part (i))
[A1] Correct unsimplified (or individual terms evaluated) answer seen Condone 1 - A + B + C leading to correct solution (for part (i))
[B1] 0.995 (for part (i))
[M1] Equation or inequality with (0.65)ⁿ and 0.01 or (0.35)ⁿ and 0.99 only (Note 1-0.99 is equivalent to 0.01 etc.) (for part (ii))
[M1] Solving their aⁿ = c, 0 < a,c < 1 using logs or Trial and Error If answer inappropriate, at least 2 trials are required for Trial and Error M mark (for part (ii))
[A1] CAO (for part (ii))

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