Question

Suppose that 48% of high school students would admit to lying at least once to a teacher during the past year and 25% of students are male and would admit to lying at least once to a teacher during the past year. Assume that 50% of the students are male. Suppose that you select a student from the subpopulation of liars. What is the probability that the student is female?

Answer 1

Let us consider,

L = A student admits of having lied at least once to a teacher

M= A student is male.

P(L)= 0.48; P(M ∩ L)= 0.25; P(M)= 0.50

We have to find P(F ∩ L) =?

Since P(M)= 0.50; So, P(F)= 1-0.50=0.50

Also, P(L)=P(L ∩ M) + P(L ∩ F)= 0.25+ P(L ∩ F) = 0.48.

So, P(L ∩ F) =0.48-0.25= 0.23

i.e. 23% of the liares are female.  

Hence P(F|L)= P(F ∩ L)/P(L) = 0.23/0.48= 0.48 is the answer.