Problem Solving

Exactly one tenth of the students at Dave’s high school are male. Exactly
one third of all seniors at his school are male. Let p be the probability
that a male at his school is a senior and let q be the probability that a
female at his school is a senior. What is the value of p/q?

(a) 4
(b) 4.25
(c) 4.5
(d) 4.75
(e) 5

let there be 100 students. 10 of them are male=>90 of them female
let x be the number of seniors. 100-x non seniors
male+senior: 1/3x; female +senior: 2/3x

p: ( a male who is a senior)=(1/3x)/10
q: (a female who is a senior)=(2/3x)/90

p/q=(1/3)*(3/2)*(1/10)*90=9/2=4.5

hence, C

scoobydooby wrote:let there be 100 students. 10 of them are male=>90 of them female
let x be the number of seniors. 100-x non seniors
male+senior: 1/3x; female +senior: 2/3x

p: ( a male who is a senior)=(1/3x)/10
q: (a female who is a senior)=(2/3x)/90

p/q=(1/3)*(3/2)*(1/10)*90=9/2=4.5

hence, C

Cool Scooby. Or for the formula wonks:

P=P(S|M)= P(S and M)/P(M) = 1/3/1/10 =10/3
Q=P(S|F)= P(S and F)/P(F) =2/3/9/10 = 20/27

P/Q= 10/3 x 27/20 =4.5

dtweah wrote:
Cool Scooby. Or for the formula wonks:

P=P(S|M)= P(S and M)/P(M) = 1/3/1/10 =10/3
Q=P(S|F)= P(S and F)/P(F) =2/3/9/10 = 20/27

P/Q= 10/3 x 27/20 =4.5

Actually, P(S and M) is 1/3 / P(S) and P(S and F) is 2/3 / P(S), but the P(S) is simplified in P/Q. I suppose you know that, but just in case.

dtweah wrote:

scoobydooby wrote:let there be 100 students. 10 of them are male=>90 of them female
let x be the number of seniors. 100-x non seniors
male+senior: 1/3x; female +senior: 2/3x

p: ( a male who is a senior)=(1/3x)/10
q: (a female who is a senior)=(2/3x)/90

p/q=(1/3)*(3/2)*(1/10)*90=9/2=4.5

hence, C

Cool Scooby. Or for the formula wonks:

P=P(S|M)= P(S and M)/P(M) = 1/3/1/10 =10/3
Q=P(S|F)= P(S and F)/P(F) =2/3/9/10 = 20/27

P/Q= 10/3 x 27/20 =4.5

I am not sure this is the right way to do it.. coz you are getting probability greater than 1 i.e. P and Q both of them are greater than 1.. I thought probability was always between 0 and 1...
So again i am really not sure.. May be you are right.. but then I dont know..

Just another approach: I didnt get this approach in the first two mins.. so agreed I would have had to pass this question if I got this in the exam..

Let the total number of males be M
Let the total number of females be F
Let the total number of Senior males be Ms
Let the total number of Senior females be Fs

According to the question:
1/10(M + F) = M (Exactly one tenth of the students at Dave’s high school are male) --------------- (1)

1/3(Ms + Fs) = Ms (Exactly one third of all seniors at his school are male) ---------------- (2)

Now P = Ms/M and Q = Fs/F

P/Q = MsF/FsM ----------- (3)

From (1) F/M = 9 and from (2) Ms/Fs = 1/2

Putting these values in (3) gives 9/2 or 4.5

so P/Q = 4.5