Out of 60 % female and 40 % male candidates appearing in an exam, 60 % candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. A candidate is randomly chosen from the qualified candidates. The probability, that the chosen candidate is a female, is :

Solution

Maths sir · 3 steps

Work with the qualified group alone: split its 60% into females and males in the ratio 2 : 1.

1. Split the qualifiers. Take all candidates as 100%, so 60% qualify. Females who qualify are twice the males who qualify. Write them as 2m and m, so 2m + m = 60% and m = 20%.
2. Who qualified. So 40% of all candidates are qualified females and 20% are qualified males. These fit inside the 60% females and 40% males, so the data is consistent.

   P(F | Q) = P(F ∩ Q)/P(Q) = 0.4/0.6 = 2/3

3. So. The chosen qualified candidate is a female with probability 2/3, option (a). The 60 : 40 split of the whole group is never needed.

The idea to keep. When the choice is made from one group only, you just need how that group splits. Check whether the given ratio already describes that group before you reach for the full Bayes formula.

Answer from the NTA final answer key. Solution by PrepWiser.