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.

(i)
(a)
\mathrm{P} (test ~postiive)

= 0.001 \times 0.995 + 0.999 \times 0.005

= 0.00599

(b)
\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

(ii)
\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.

Comments
    pingbacks / trackbacks

    Leave a Comment

    two × five =

    Contact Us

    CONTACT US We would love to hear from you. Contact us, or simply hit our personal page for more contact information

    Not readable? Change text. captcha txt

    Start typing and press Enter to search