Jrahs 95 - Q8b (1 Viewer)

[sHin]

A school is divided in 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 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



I can't seem to be able to get part ii). Any help appreciated. Thanks.

 

[mojako]

Note: answer may not be correct..

(i)
700/1300 * 200/600 + 600/1300 * 400/700

(ii)
1/2 * (400/700 + 400/699)
(I'm taking average of the two cases.. not sure if it can be done..)

waiting for authoritative answer...

EDIT: part (ii) is incorrect, keep scrolling.....

 

[sHin]

The answer for part 1 is correct. However, according to the answer sheet, the answer to part 2 is suppose to be 49/76,

 

[Jago]

is the answer to the 2nd part 21/169?

 

[mojako]

I think it shud be 7/13,
because for the second student to be from Senior,
the first must be from Junior.
P(first from Junior) = 700/1300 = 7/13

 

[Li0n]

err wtf ...
wait

 

[smallcattle]

umm i think the question asked IF the second person is a boy, then he must be a senior

i interpreted the question as P(the second person is not a boy)+P(If the second person is a boy, he is a senior)

but i cant get the answer there

121/273 + 700/1300 * 400/600 just isnt working..

 

[Li0n]

Note: answer may not be correct..
(ii)
1/2 * (400/700 + 400/699)
(I'm taking average of the two cases.. not sure if it can be done..)

waiting for authoritative answer...

i think that you think that when a girl is picked first then a boy MUST be picked second, (by the looks of your working), i dont think thats the case :/
Annoying question though i dont think its worded that well :S

 

[mojako]

i think that you think that when a girl is picked first then a boy MUST be picked second, (by the looks of your working), i dont think thats the case :/
Annoying question though i dont think its worded that well :S

no [EDIT: maybe yes.. I didn't really get what he meant], I thought:
if the boy is picked for the second student,
400/700 is for he to be from Senior when the first student is not a boy (so there are still 700 boys total).
400/699 is for he to be from Senior when the first student is a boy.
(400 is the number of boys in Senior)

But that is wrong anyway.
Now I really believe it's 7/13 (see my other post).

 

[chazza]

dont you just do this

(junior / total students) x (senior boys/ total senior)

700/1300 x 400/600 = 28/78
= 14/39

i dunno...

 

[Li0n]

no, I thought:
if the boy is picked for the second student,
400/700 is for he to be from Senior when the first student is not a boy (so there are still 700 boys total).
400/699 is for he to be from Senior when the first student is a boy.
(400 is the number of boys in Senior)

But that is wrong anyway.
Now I really believe it's 7/13 (see my other post).

vvvv

(junior / total students) x (senior boys/ total senior)

700/1300 x 400/600 = 28/78
= 14/39

thats what i had first, it seems more logical than the 7/13 one since there is still the choice of the boy and girl. But the answer isn't right :?

 

[KungPow]

Yeah i got 14/39 as well using the same numbers.

Maybe I'm misinterpreting the question though.

Seems a bit more complicated by the wording of the question "if the second student chosen is a boy, he is from the senior school". Not sure, I can't really imagine the question properly

 

[mojako]

any help?
*looking to Jrah students on the forum... especially the 4U ones*

maybe the given answer is wrong after all....

 

[Estel]

not a JR student mojako, but lets see

i)
7/13*1/3 + 6/13*4/7 = 121/273

ii)
P(boy from senior school)= 7/13*4/6 = 14/39
P(boy from junior school)= 6/13*3/7=18/91
It follows that the required probability is 49/76

 

[chazza]

not a JR student mojako, but lets see

i)
7/13*1/3 + 6/13*4/7 = 121/273

ii)
P(boy from senior school)= 7/13*4/6 = 14/39
P(boy from junior school)= 6/13*3/7=18/91
It follows that the required probability is 49/76

how does it follow the required probabilty of 49/76???
can you show your working out?

thanks

 

[Estel]

how does it follow the required probabilty of 49/76???
can you show your working out?

thanks

(14/39)/(14/39+18/91) = 49/76

 

[Li0n]

heh, like i said
shitty worded question.
ii) if the second student chosen is a boy, he is from the senior school

i thought he HAD to be a boy FROM the senior school

way to go english & maths.

 

[mojako]

hmm.. but whats flawed in my argument??
that P(if its a boy, its from senior)
= P(first student is from junior)
= 7/13
??

also, 7/13 < 49/76
and this really makes me confused...
if first student isnt from junior, the second cant be from senior... but the probability that the first student is from junior is 7/13

 

[withoutaface]

i) 7/13*1/3+6/13*4/7

ii) P(boy senior)= 7/13*2/3
P(boy junior)= 6/13*3/7

answer (7/13*2/3)/(7/13*2/3+6/13*3/7)

Ok?

 

[Li0n]

i have a better method
1/76 + 43/76 + 6/76 = 49/76
KEKKEKEK