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

Practise IB Mathematics HL 4.6 by applying combined, conditional and independent events methods to questions from the Question Bank.

Exam points

Represent combined events with Venn, tree and sample-space diagrams or outcome tables, and calculate P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
Use conditional probability and independence for dependent or independent events, handling with- and without-replacement assumptions explicitly.

[Maximum number: 4]

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 Questions question 1