2011 A-level H2 Mathematics (9740) Paper 2 Question 7 Suggested Solutions

By KS Teng

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

(i)
Firstly, the number of different friends is a fixed constant.
Secondly, the probability of successfully contacting a friend is constant.

(ii)
The probability of contacting a friend will vary from friend to friend, as some friend might not be free or contactable during that evening.

(iii)
\mathrm{R} \sim \mathrm{B}(8,0.7)

\mathrm{P}(R \ge 6) = 1 - \mathrm{P}(R \le 5) \approx 0.552

(iv)
\mathrm{R} \sim \mathrm{B}(40, 0.7)

Since n = 40 \mathrm{~is~large,~} np = 28 > 5 \mathrm{~and~} nq = 12 > 5 ~ \mathrm{R} \sim \mathrm{N}(28, 8.4) \mathrm{approximately}

\mathrm{P}(R \textless 25)

= \mathrm{P}(R \textless 24.5) by continuity correction

\approx 0.114

KS Comments:

Students should be careful to write all assumptions in the context of question. I cannot stress the importance of this. Conditions for Binomial Approximation have to be well stated and explained. Lastly, remember to do continuity correction.

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