enter image description here

I solved the problem. I am getting the final answer as 8/15, however, the book says the answer is 7/15.Seems like they haven't subtracted 7/15 from 1 Please help.

  • 1
    $\begingroup$ Can you show your calculations? $\endgroup$ – Bram28 Oct 17 '17 at 19:28

Let $B$ be the event that a person is a boy. Let $M$ be the event that a person score more than $40$ marks. We are told $Pr(B)=0.6, Pr(M)=0.6, Pr(M\mid B^c)=0.8$. We are tasked with calculating $Pr(M^c\mid B)$.

Continuing to build a list of possibly useful numbers: $Pr(M\cap B^c)=Pr(B^c)Pr(M\mid B^c)=0.4\cdot 0.8=0.32$

$Pr(M\cap B)=Pr(M)-Pr(M\cap B^c)=0.6-0.32=0.28$

$Pr(M^c\cap B)=Pr(B)-Pr(M\cap B)=0.6-0.28=0.32$

$Pr(M^c\mid B)=\frac{Pr(M^c\cap B)}{Pr(B)}=\frac{0.32}{0.6}=\frac{8}{15}$

My answer agrees with yours.


We have $60\%$ boys and $40\%$ girls.

We know $20\%$ of the girls have less equal $40$ points, these are $8\%$ of the students.

We know $40\%$ of the students have less equal $40$ points.

So the boys which have $40$ or less points are $32\%$ of the students, these are $32/60 =8/15$ of the boys.

Hm, that information about the range $0$ to $150$ marks seems not to matter. No idea how to reduce to $7/15$.


Let there be 100 students in a class.

60 are boys, 40 girls.

32 girls scored more than 40 points.

60 boys and girls scored more than 40.

$\rightarrow$: 28 boys scored more than 40.

$\rightarrow $: 32 boys scored 40 or less.

Fraction : 32/60= 8/15.

Answer: 8/15 of the boys scored 40 marks or less.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.