2014 A-level H1 Mathematics (8864) Question 11 Suggested Solutions

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

(i)

$\mathrm{P} (L) = \frac{90}{290+x}$

$\mathrm{P} (G) = \frac{100}{290+x}$

Since L and G are independent events,

$\mathrm{P} (L \cap G) = \mathrm{L} \times \mathrm{G}$

$\frac{30}{290+x} = (\frac{90}{290+x})(\frac{100}{290+x})$

$x = 10$

(ii)
$\mathrm{P} (L \cup T) = \frac{235}{300} = \frac{47}{60}$

(iii)

$\mathrm{P} (T \cap G) = \frac{142}{300} = \frac{71}{150}$

(iv)

$\mathrm{P} (L | G) = \mathrm{P}(L)$ since L and G are independent events.

$\therefore, \mathrm{P} (L | G) = \frac{90}{300} = \frac{3}{10}$

(v)

Required Probability $= \frac{37}{300} \times \frac{36}{299} = 0.0148$

KS Comments

Some students commented that (v) should be done via binomial distribution, but this is a misguided approach as they should realise that the probability is not constant. Thus, a binomial model will not be appropriate.

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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.

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SomeGuy April 8, 2024
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Typo in question 1, as your equation writes 10/(290+x) instead of 100/(290+x)
- KS Teng April 9, 2024
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  Thank you 🙂

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2014 A-level H1 Mathematics (8864) Question 11 Suggested Solutions

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