2015 A-level H2 Mathematics (9740) Paper 2 Question 6 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
Let X denote the number of red sweets in a small packet of 10 sweets.

X \sim \mathrm{Bin} (10, 0.25)

\mathrm{P}(X \ge 4) = 1 - \mathrm{P}(X \le 3) \approx 0.224 (3 SF)

(ii)
Let Y denote the number of red sweets in a large packet of 100 sweets.

Y \sim \mathrm{Bin} (100, 0.25)

Since n is large, np = 25 > 5, n(1-p) = 75 > 5

Y \sim \mathrm{N}(25, 18.75) approximately

\mathrm{P}( Y \ge 30) = \mathrm{P}(X > 29.5) by continuity correction
\approx 0.149 (3 SF)

(iii)
Let W denote the number of packets out of 15 packets that contain at least 30 red sweets.

Y \sim \mathrm{Bin}(15, 0.1493487984)

\mathrm{P}( W \le 3) \approx 0.825 (3 SF)

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