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.

About

KS Teng

KS has been teaching H2/H1 Mathematics and IB mathematics for the more than 10 years. Having taught students from all various Junior Colleges, KS adapts to students' abilities and help them better understand the topics. As someone who loves to teach mathematics and sees it as a truly useful tool in life, KS seeks to enable students to appreciate math. Therefore, his tuition mission is to motivate and cultivate students to be independent and confident thinkers.

Comments

pingbacks / trackbacks

2012 A-level H2 Mathematics (9740) Suggested Solutions | The Culture
[…] Question 5 (Note Worthy) […]
August 17th, 2015 10:42 AM

Cart

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

KS Comments:

Leave a Reply to 2012 A-level H2 Mathematics (9740) Suggested Solutions | The Culture Cancel reply