IB Maths AA SL 4.6 Combined, conditional and independent events Question Bank

Practise IB Mathematics SL/HL 4.6 by applying combined, conditional and independent events methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[Maximum number: 6]

A nationwide study on reaction time is conducted on participants in two age groups. The participants in Group X are less than 40 years old. Their reaction times are normally distributed with mean 0.489 seconds and standard deviation 0.07 seconds.

A randomly selected participant has a reaction time greater than 0.65 seconds. Find the probability that the participant is in Group X.

correct work for P (group X and t>0.65 ) or P (group Y and t>0.65 ) (may be seen anywhere)
eg P( group X $) \times \mathrm{P}(t>0.65 \mid \mathrm{X}), \mathrm{P}(X \cap t>0.65)=0.0107 \times 0.38(=0.004075)$ , $\mathrm{P}(Y \cap t>0.65)=0.396 \times 0.62$
recognizing conditional probability (seen anywhere)
eg $\mathrm{P}(\mathrm{X} \mid t>0.65), \mathrm{P}(A \mid B)=\frac{\mathrm{P}(A \cap B)}{\mathrm{P}(B)}$
valid approach to find P(t>0.65)

Figure for Answer to Question SL 4.6—Combined, conditional and independent events question 1 — IB Maths AA SL

correct work for P(t>0.65)
eg $\quad 0.0107 \times 0.38+0.396 \times 0.62,0.249595$
correct substitution into conditional probability formula
eg $\frac{0.0107 \times 0.38}{0.0107 \times 0.38+0.396 \times 0.62}, \frac{0.004075}{0.249595}$
0.016327
$\mathrm{P}(\mathrm{X} \mid t>0.65)=0.0163270$

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SL 4.6—Combined, conditional and independent events question 1