CAIE A-Level Mathematics A2 5.3.4 Elementary Probability Questions

Practise solving conditional probability problems with tables, tree diagrams and dependent events.

Exam points

calculate conditional probabilities from tables and event information
construct and use tree diagrams for dependent selections
solve multi-stage conditional probability problems

[Maximum number: 4]

The independent random variables X and Y have the distributions $\operatorname{Po}(1.9)$ and $\operatorname{Po}(2.2)$ respectively．

Find the probability that X=2 given that X+Y<4 ．

P(X+Y<4 and X=2)=P(2,0 or 2,1)
Stated or implied.

$=\mathrm{e}^{-1.9} \times \frac{1.9^{2}}{2}\left(\mathrm{e}^{-2.2}+\mathrm{e}^{-2.2} \times 2.2\right)$ 0.0957]
$\mathrm{P}(X=2 \mid X+Y<4)=\frac{{ }^{\prime} 0.0957^{\prime}}{{ }^{\prime} 0.414^{\prime}}$
Attempt $\frac{\mathrm{P}(X+Y<4 \text { and } X=2)}{\mathrm{P}(X+Y<4)}$ . Prob for denominator can be found in (a).

0.231 ( 3 sf )
4

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CAIE A-Level Mathematics A2 5.3.4 Elementary Probability Questions question 1