Tricky probability question (1 Viewer)

[porcupinetree]

Could someone please help me with this question? The answers say 2/7, but they aren't very enlightening as to why this is the case.

Thanks

 

[InteGrand]

Could someone please help me with this question? The answers say 2/7, but they aren't very enlightening as to why this is the case.

Thanks

 

[porcupinetree]

Cheers dude, I'd rep you but bos won't let me

 

[braintic]

The answer is NOT 2/7, it is 4/9.

The answer of 2/7 is the probability that both are black given that one is black.
This question is asking for the probability that both are black given that a SPECIFIC one is black.

Bayes Theorem would confirm this answer.

 

[InteGrand]

Yeah I was thinking 4/9 too...and I also used Bayes Theorem to confirm lol. (This was why I avoided saying the answer is 2/7.)

 

[braintic]

Yeah I was thinking 4/9 too...and I also used Bayes Theorem to confirm lol.

It is the same issue as in the 1997 2 unit HSC Q9a(iv).

The correct answer is 1/3. At the time the answer that was marked correct was 1/5, and this incorrect answer still appears in many published solutions.

It took MANSW 10 years to finally issue the correct solution to this question.

 

[InteGrand]

It is the same issue as in the 1997 2 unit HSC Q9a(iv).

The correct answer is 1/3. At the time the answer that was marked correct was 1/5, and this incorrect answer still appears in many published solutions.

It took MANSW 10 years to finally issue the correct solution to this question.

What happens in HSC marking if these types of Q's appear in the paper (with erroneous answers provided)?

 

[braintic]

What happens in HSC marking if these types of Q's appear in the paper (with erroneous answers provided)?

Nothing can happen if the problem is not fixed for 10 years. The marks stand.

Even at the time, we didn't know there was a problem until well after the results came out, because we were unaware of what their answer was until solutions came out.

I always wonder if there were markers that year who knew they were marking it wrongly, but had no choice in the matter because they had been instructed by the head marker what to mark correct. If it were me, I would feel the need to resign rather than mark BS.

 

[InteGrand]

Speaking of conditional probability, I thought that was something that's not in the HSC Syllabus? And if it is in the syllabus, they should put in Bayes' Theorem too.

 

[braintic]

Speaking of conditional probability, I thought that was something that's not in the HSC Syllabus? And if it is in the syllabus, they should put in Bayes' Theorem too.

It is not specifically in the syllabus. But neither the HSC question nor the one here needs Bayes theorem to work them out.
This one involves just removing one black (the one in his hand), so 4 of the remaining 9 jellybeans are black.
All conditional probability involves a reduction in the size of the sample space.
This simplified version of conditional probability is now specifically mentioned in the new Stage 5 syllabus (years 9/10).

 

[Trebla]

An application of conditional probability kinda exists in the syllabus through sampling without replacement problems

 

[InteGrand]

I'm guessing though a lot of HSC students wouldn't know what you were referring to if you mentioned "conditional probability" to them.

 

[Drongoski]

An application of conditional probability kinda exists in the syllabus through sampling without replacement problems

True

 

[braintic]

An application of conditional probability kinda exists in the syllabus through sampling without replacement problems

Yes, any condition that reduces the sample space is conditional probability.

 

[Drsoccerball]

Is the answer 2/7 or 4/9

 

[calamebe]

Is the answer 2/7 or 4/9

Well Braintic and Integrand said 4/9 and that's the only logical answer to me.

 

[Drsoccerball]

Well Braintic and Integrand said 4/9 and that's the only logical answer to me.

I initially got that but integrands working makes sense as well

 

[braintic]

I initially got that but integrands working makes sense as well

As I said earlier, Integrand's working is correct for a different question.
ie. If someone tells you that ONE of the jellybeans is black (but not which one), then the answer IS 2/7.

Since we are specifically told that the jellybean in his hand is black, the answer is 4/9.

 

[dan964]

To summarise
2/7 is the probability of at least one jellybean being black, but doesn't guarantee that the one in the hand is black, as afore mentioned by braintic.
4/9 is the chances of picked one black - we ignore the black one in the hand but note there are 9 jellybeans the second hand could contain of which 4 (not 5 as one is removed), are black.

Is this from a particular task?
the later is needed

 

[si2136]

4/9.

There are 5B, 3R and 2Y.

If he takes out 2, there would be 8 left.

One is B, so it would be 4B, 3R and 2Y (9 Jellybeans)

Therefore 4/9