Is it just me or is this an odd way to word this math problem

[Bubbleawsome]

EDIT
Here is the question

The probability that a dessert sold in a certain cafe contains chocolate is 86%. The probability that a dessert containing chocolate also contains nuts is 30%. Find the probability that a dessert chosen at random contains nuts given that is contains chocolate. Round to the nearest tenth of a percent.

That is exact. Answer was

Spoiler

34.9%

. Formula is probability of a and b over probability of b. Or

P(A and B)
P(B)

Old post below


Here's the question as well as I can remember it.

86% of sweets a bakery sells contain chocolate. 30% of these chocolate sweets contain nuts. What is the probability that a sweet will contain nuts given that it contains chocolate.

I thought that if it contains chocolate then j should go back to that 30%. That wasn't right, so I tried multiplying .86 by .3 to get the total percent of chocolate nut candies they sell. Also not right.

So I guessed.

EDIT: 86% not 80%

What do you guys think? Am I just bad at math and logic, or is this a weird question?

 

[zinfamous]

my head tells me that it's ~27% of the candies in that store that contain nuts.

oh wait that's not right--I'm still ignoring the 20% that are not part of my calculation. ...I think.

You know what? I'm long done with the SAT. fuck this.

 

[tynopik]

you're not remembering the question correctly

 

[Smoblikat]

I got roughly 25.8% of the candy contains nuts, but im probobly quite wrong.

 

[Imp]

I bombed college statistics... FML, never got this stuff or bothered to try.

 

[clamum]

It seems like kind of a trick question to me.

What is the probability that a sweet will contain nuts given that it contains chocolate?

The way I look at it, it gives me that the sweet contains chocolate ("given that it contains chocolate"). So the probability it will contain nuts is, as it stated, 30%. Looks like I'm wrong judging from the other responses but that's what made sense to me.

 

[tynopik]

I thought that if it contains chocolate then j should go back to that 30%. That wasn't right

It is right for the question as stated

What is the probability that a sweet will contain nuts given that it contains chocolate.

We can rephrase this as

What is the probability that a chocolate sweet will contain nuts

it literally spells out the answer in the previous sentence

30% of these chocolate sweets contain nuts.

the only way it's not 30% is if they want it written as .30
(or you got the question wrong, which seems more likely, because they wouldn't ask such a basic question)

 

[DaveSimmons]

I think you're misremembering the question, or it's a trick question.

Maybe I need more coffee, but if you are considering only the subset of sweets that are chocolates ("given that it contains chocolate.") and you have just been told the probability for that subset is 30%, then the probability is 30%.

To answer anything about sweets as a whole, we don't have enough information. What is the probability for nuts in NON-chocolate sweets? Like a Payday bar or "nut log" / "nut rolls" (nougat covered in nuts), or glazed pecans, or....

 

[zinfamous]

It seems like kind of a trick question to me.



The way I look at it, it gives me that the sweet contains chocolate ("given that it contains chocolate"). So the probability it will contain nuts is, as it stated, 30%. Looks like I'm wrong judging from the other responses but that's what made sense to me.

right, that statement is essentially superfluous because any sweet with nuts is already going to contain chocolate. It is required to.

But you aren't looking at 30% (the question is asking about % of total candies in the store).

You are looking at 30% of 80%. I *think* that is all, but I am not exactly sure if simply calculating that (~1/3rd of 80) accounts for the remaining 20% of the non-chocolate candies.

I *think* it does, but fear and math-loathing tells me otherwise.

EDIT: I'm wrong. tynopik is right ^ >

 

[zinfamous]

It is right for the question as stated



We can rephrase this as
What is the probability that a chocolate sweet will contain nuts


it literally spells out the answer in the previous sentence



the only way it's not 30% is if they want it written as .30
(or you got the question wrong, which seems more likely)

You know what, you are right. "given that" not only requires the candy to contain chocolate (all nuts candies already do), but the question is actually only asking about the chocolate candies that contain nuts.

Which is directly spelled out. That was my first thought as well, but I tossed it immediately because I thought the trick was in assuming the trick.

stupid trick question.

 

[jchu14]

It is right for the question as stated



We can rephrase this as


it literally spells out the answer in the previous sentence



the only way it's not 30% is if they want it written as .30
(or you got the question wrong, which seems more likely, because they wouldn't ask such a basic question)

I agree, though it's possible that this question is just the first question in a series of questions. For example, I could see the next question being: Assume 20% of the non-chocolate sweets also contain nuts, what's the probability of the the sweet contain nuts given that it contains chocolate?

As written, I also agree that it's 30%.

 

[dullard]

You all are assuming that the sweet in question was produced by the bakery that was discussed. I see no reason other than the "jumping-to-conclusions" reason to assume that is the case.

There is not enough data in the OP to know the probability that "A sweet" will have nuts. We could determine the probability that "a sweet randomly chosen from the bakery described" will have nuts.

 

[TallBill]

30%, dunno how this is even debatable. Then again I got 109% in my logic class without going to any lectures.

 

[DaveSimmons]

I agree, though it's possible that this question is just the first question in a series of questions. For example, I could see the next question being: Assume 20% of the non-chocolate sweets also contain nuts, what's the probability of the the sweet contain nuts given that it contains chocolate?

As written, I also agree that it's 30%.

Which would be a second trick question -- if you know it is a chocolate, it doesn't matter what the % is for non-chocolate sweets

It would be funny if this was a pop quiz and there were 4-5 questions like that.

Assume 100% of the sweets without chocolates contain nuts ...

30%

If cobras are also in the shop biting people ...

30%

 

[Rakehellion]

You didn't read the question correctly.

 

[Bart*Simpson]

86% of sweets a bakery sells contain chocolate. 30% of these chocolate sweets contain nuts. What is the probability that a sweet will contain nuts given that it contains chocolate.

Give a candy to the gimpy kid with the nut allergy and see if he goes into anaphylactic shock and then has a seizure.

The probability that the one candy you pick for him will be the one that sends him to the emergency room and gets you sent to jail is about 99.9999%

 

[ElFenix]

it's 30%. the intent of the question is to make you waste time while you overthink it so that you don't have time to finish the section. those SAT test makers are sneaky bastages.

 

[Ruptga]

If .3 and .86*.3 are both wrong, then the test is fucked. That said, it is totally within the realm of possibility that the test is fucked; word problems like this are known for being literally impossible.

 

[jchu14]

Which would be a second trick question -- if you know it is a chocolate, it doesn't matter what the % is for non-chocolate sweets

It would be funny if this was a pop quiz and there were 4-5 questions like that.

Assume 100% of the sweets without chocolates contain nuts ...

30%

If cobras are also in the shop biting people ...

30%

OOPS, i meant what's the probability of the a piece of sweet is chocolate given that it contains nuts.

 

[Bubbleawsome]

I asked the teacher about it and he said to use the formula

probability of A and B (chocolate and nuts) divided by probability of nuts.

Considering I wasn't told the probability of nuts when it isn't chocolates I assumed I had to do (.86*.3)/.86 which would be the same .3 I assumed. That wasn't an answer choice. I ended up guessing the answer closest to .86*.3. That comes out to .258 but the only choice close to that was .287.

As for the question; I know I got the numbers right, and I'm fairly sure I got the logic of the question right. It was a 20 question multiple choice so I should have it back soon, and I'll post about it again.

 

[Rakehellion]

it's 30%. the intent of the question is to make you waste time while you overthink it so that you don't have time to finish the section. those SAT test makers are sneaky bastages.

No, the question was worded as he remembered it. He got the answer wrong.

 

[gorcorps]

I think trick question too

30% given how you wrote it

 

[Bubbleawsome]

No, the question was worded as he remembered it. He got the answer wrong.

Probably. We'll know in a couple days lol

 

[DigDog]

30% or the question is worded reeeeally badly.

the numbers are irrelevant:

86% of sweets a bakery sells contain chocolate. ALL of these chocolate sweets contain nuts. (ergo chocolate = nuts) What is the probability that a sweet will contain nuts given that it contains chocolate=nuts. 100%


now change the numbers back

86% of sweets a bakery sells contain chocolate. 30% of these chocolate sweets contain nuts. (ergo chocolate = 30%nuts) What is the probability that a sweet will contain nuts given that it contains chocolate=nuts. 30%

you could argue that the remaining 14% of the sweets are uncategorized and could potentially contain nuts even if they do not contain chocolate; however you cannot omit a portion of the equation and then ask for an answer.

I wouldn't be surprised if the question was actually wrong in the first place.

 

[Cheesemoo]

It seems like kind of a trick question to me.



The way I look at it, it gives me that the sweet contains chocolate ("given that it contains chocolate"). So the probability it will contain nuts is, as it stated, 30%. Looks like I'm wrong judging from the other responses but that's what made sense to me.

this,

these questions are always dependent on how they are asked.