Probability Ques...JR (1 Viewer)

[jsttesting]

Hey guys,

I came across a probability question in the James Ruse 1995 Trial Paper (Ques 8b). I got the first part (Answer is 121/273), but I couldn't get the second part. The question is:

A school is divided into two parts: Senior school with 400 boys and 200 girls and Junior school with 400 girls and 300 boys. A first student is chosen at random from the whole school. If this student comes from the Junior school, a second student is chosen from the Senior school; if the first student comes from the Senior school, then a second student is chosen from the Junior school. By making use of a tree diagram, or otherwise, find the probability that:

i) the second student chosen will be a girl;
ii) if the second student chosen is a boy, he is from the senior school.

Any answers would be most appreciated....

 

[SaHbEeWaH]

you've already worked out that P(2nd student = girl) = 121/273
so, P(2nd student = boy) = 1 - 121/273 = 152/273
now we need the P(2nd student = senior boy)

draw up your probability tree.
find the branches that end with a senior boy
do the calculations you should end up with something like:
P(B_j, B_s) = 3/13 * 4/6 = 2/13
P(G_j, B_s) = 4/13 * 4/6 = 8/39

so P(2nd student = senior boy) = 14/39

so the probability of the second boy being senior, knowing that he's a boy is

(senior boy)/(all boy)
(14/39)/(152/273) = 49/76

 

[jsttesting]

Oh ok, I think i get it now. I did think of getting the sample space for the number of boys earlier on, but never tried it. Anyways, thanks