2012 A-level H2 Mathematics (9740) Paper 2 Question 5 Suggested Solutions

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

\mathrm{P} (test ~postiive)

= 0.001 \times 0.995 + 0.999 \times 0.005

= 0.00599

\mathrm{P} (disease~ | ~test positive)

\frac{\mathrm{P} (disease ~\cap~ test positive)}{\mathrm{P}(test ~positive)}

\frac{0.001 \times 0.995}{0.00599}

\approx 0.166

\mathrm{P}(disease~ |~ test positive ) = 0. 75

\frac{\mathrm{P} (disease ~\cap~ test positive)}{\mathrm{P}(test~ positive)} = 0.75

\frac{0.001p}{0.001p + 0.999(1-p)} = 0.75

Using the Graphing Calculator, p \approx 0.999666

KS Comments:

Students will find it helpful to start this question with a tree diagram.

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