IB Maths AA SL 4.6 Combined Conditional and Independent Events Topic Practice

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)

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
$\mathrm{P}(\mathrm{X} \mid t>0.65)=0.0163270$