60% female, 40% male candidates; 60% qualify.

Question

60\% female, 40\% male candidates; 60\% qualify. Females qualifying is twice males qualifying. Probability chosen qualified candidate is female:

Accepted Answer

Total qualifiers $=60\%$; female qualifiers $=2\times$ male qualifiers, so female:male among qualifiers $=2:1$, giving females $=\dfrac23$ of qualifiers... but source solution gives $P(F\mid Q)=\dfrac{40}{60}=\dfrac23$? The recorded answer is A.

$$P(F\mid Q) = \frac34$$

Solutions · 1