Jrahs 95 - Q8b (1 Viewer)

[withoutaface]

Nope. for two reasons:
1. you're just repeating Estel and in fact made it more confusing since u used 2/3 not 4/6
2. you r not allowed to use the word "Ok?" because its copyrighted

I cbf reading the thread, but I knew there were a million responses and I was just confirming which was the right one

 

[Smiley :D CvH]

hey but it doesnt say dat it a must b a junior girl or boy 2 have da first selection n u jsut listed the probability of junior boy

 

[mojako]

hey but it doesnt say dat it a must b a junior girl or boy 2 have da first selection n u jsut listed the probability of junior boy

for the second person to be chosen from senior, the first person must turn out to be from junior.
read the question carefully

 

[Smiley :D CvH]

Answer

i got dis msg from meh fren :

Majoka is rite… read the question and notice that the student is from one side of the skool then the next chosen must be from the other… ie junior then senior
Use ur tree diagram wif 4 stems representing senior b and g and junior b and g and ull get:
P(j gb) = 4/13 + 3/13
And from there P(senior boy) = 4/6(4/13 + 3/13)
The an scums out to b 14/39… im pretty sure this is rite

 

[mojako]

i got dis msg from meh fren :

Majoka is rite… read the question and notice that the student is from one side of the skool then the next chosen must be from the other… ie junior then senior
Use ur tree diagram wif 4 stems representing senior b and g and junior b and g and ull get:
P(j gb) = 4/13 + 3/13
And from there P(senior boy) = 4/6(4/13 + 3/13)
The an scums out to b 14/39… im pretty sure this is rite

Just wanna make sure that everyone knows that the proper answer is
49/76

and that I wasn't completely right.

Estel was the first one who knew how to work out the correct answer.

 

[ArchAngelometal]

hi im smileys frend,
i jus wana know y u "think" 49/76 (ie 64.5%) is the ans???
when uve got 4 total possible outcomes for the senior boy that give in this situation closer to 25%. This still holds tru is u eliminate 2 of them after the first selection... meaning that 50% of the remaining outcomes can b of that.. but over all its still closer to 25%....
my ans is a lil higher than 25%... more like 34%... which is very close to what it should b if im wrong

i think wat uve done is ignored the 2 u eliminate from the top half of the tree including the senior as the first selection...

 

[mojako]

The ans of 49/76 is what appears in the answer key for this paper, so it's definitely right.

if uve been reading this whole thread (yes there are lots of posts...)
youll know that what part (ii) of the Q asks is the probability that the second student is from senior, IF it turns out to be a boy.
So we're not counting the probability that it will be a boy. We just need it to be from senior since we are given that its a boy.

EDIT: The following should now be ignored. Read the last few posts instead.
---------------
In the following, "it" refers to the second student.
P(its a boy and from senior) = P(its a boy) * P(its from senior [given its a boy])
We need the P(its from senior) one.

P(its a boy and from senior)
= 14/39 (the thing you got in your answer)
P(its a boy)
= 1 - P(its a girl), and P(its a girl) is found in part(i) of the question
= 152/273

So, 14/39 = 152/273 * P(its from senior).
---------------

 

[ArchAngelometal]

so basically... were takin the girls out of the eq and starting fresh with the "left overs" and finding if hes senior?

 

[mojako]

so basically... were takin the girls out of the eq and starting fresh with the "left overs" and finding if hes senior?

yes.
well the girls are not taken out of the school/classroom, but they're not in the eqn becoz its the probabilty that the second student will be from senior if he/she turns out to be a boy.
EDIT: the girls ARE taken into account.

 

[Estel]

So perhaps the moral of the story is that you should all read the question before answering it

 

[mojako]

So perhaps the moral of the story is that you should all read the question before answering it

and can u tell me whats wrong with my logic?
for the second student to be from senior, the first must be from junior
P(first from junior) = 7/13
P(second from senior) = P(first from junior)

this Q is somewhere in a previous post

please...
(well I hope I get some insight which I can use for my maths exams)

 

[Estel]

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

That is the probability of the 2nd student being senior, full stop.
In other words P(girl 2nd) + P(boy 2nd) = 7/13.
P(girl 1st) + P(boy 1st) = 6/13
suppose P(g2) = a, P(b2) = x, P(g1) =c, P(b1) = y
The question says only b2 or b1 is possible.
What you have done is say then P(b2) = x+a, and P(b1) = c+y.

Your logic: pick senior or junior, and that student will be a boy.
It assumes that the choice of senior or junior will not be affected by the fact the 2nd student will be a boy.

This comes back down to depedent variables. You cannot do what you have done because the probability of choosing senior/junior is affected if we know that the 2nd MUST be a boy.

Ahh... this is too hard.
I will think about this, I know I have given an unsatisfactory answer.

 

[velox]

ill try it tommorrow and ill see what i can do

 

[mojako]

If you're still interested to know how to do this question:

Before I tried to use the product rule,
P(its a boy and from senior) = P(its a boy) * P(its from senior [given its a boy])
but it's best NOT to think about it that way because product rule is used for independent events. In this one, having a second student as a boy will affect the number of students eligible to be selected and changes the probability that it's from senior.

You should use the concept of comparing probabilities, to find the probability that something happens given that another thing happens.
P(the second student is from senior, given it's a boy)
= P(the second student is from senior and is a boy) / P(the second student is a boy)
= P(what we want, i.e. a senior boy) / P(the given condition, i.e. a boy)

Also, in this sense we've taken into account that the student can be a girl because it's picked randomly. So the girls are not ignored.

The answer we get, 49/76, is exactly what the wording implies: the probability that it's from senior if it's a boy. For example, you're a friend of a maths teacher who chose the students at random. Your friend told you that today the second student he selected was a boy, and he also told you the composition of the student body in the school. He then asked you the chances of the boy being from senior and promised to give you a prize if you get this right. You answered that it's 49/76, and you got a prize.

Is this relevant to you? Probably yes.
When the question use the key words "given" and "if",
use this concept.

Thanks to Estel and withoutaface who helped me understand this concept in another thread.