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Study SL 4.6—Combined, conditional and independent events conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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Amanda enters data from surveys into a database. It can be assumed that the accuracy of any survey entered is independent of all other surveys entered.
From previous records, it is known that Amanda enters 8 % of the surveys inaccurately.

Find the value of x.

METHOD 1

\begin{aligned} & \mathrm{P}(I \mid C)=\frac{x}{100} \text { (seen anywhere) } \\ & \mathrm{P}(I)=0.55 \times 0.08+0.25 \times 0.06+0.2 \times \frac{x}{100} \end{aligned}

equating their expression for P(I) to $\frac{x}{100}$

\begin{aligned} & \frac{x}{100}=0.55 \times 0.08+0.25 \times 0.06+0.2 \times \frac{x}{100} \\ & x=7.375 \\ & x=7.38 \text { (accept } 7.38 \% \text { ) } \end{aligned}

METHOD 2

\mathrm{P}(I)=0.55 \times 0.08+0.25 \times 0.06+0.2 \times y

equating their expression for P(I) to y
$y=0.55 \times 0.08+0.25 \times 0.06+0.2 \times y$
y=0.07375
recognizing to multiply their y value by 100
x=7.38 (accept 7.38 % )

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IB Maths AA HL Sl 4 6 Combined Conditional and Independent Events Topic Practice

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Question 1