IB Maths AA HL Sl 4 11 Formal Conditional Probability Questions

Practise IB Mathematics HL 4.11 by applying formal conditional probability methods to questions from the Question Bank.

Exam points

Calculate conditional probability with P(A|B) = P(A ∩ B)/P(B), and rearrange to use P(A ∩ B) = P(B)P(A|B) in a stated sample space.
Test independence by comparing P(A|B) with P(A) or P(A ∩ B) with P(A)P(B), interpreting the conclusion in context.

[Maximum number: 3]

The random variable X has probability distribution $\operatorname{Po}(8)$ .

Find $\mathrm{P}(X=6 \mid 5 \leq X \leq 8)$ .

$\mathrm{P}(X=6 \mid 5 \leq X \leq 8)=\frac{\mathrm{P}(X=6)}{\mathrm{P}(5 \leq X \leq 8)}=\frac{0.122 \ldots}{0.592 \ldots-0.0996 \ldots} =0.248$

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