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

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Well? (MULTIPLE CHOICE!)

  • Question was stupid

  • Bubbleawsome was stupid

  • I couldn't tell you, I'm bad at math

Results are only viewable after voting.
DaveSimmons said:
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....
Click to expand...


That would be my answer a well -- in fact they give you the answer in the question...


Brian
 
tynopik said:
pic plz

not that we don't trust you to transcribe it accurately, but . . .
Click to expand...
Can't take pictures of a test, sorry. I copied it into my notes though, so here it is

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.
Click to expand...

That is exact. Answer was
34.9%
. Formula is probability of a and b over probability of b. Or

P(A and B)
P(B)
 
Bubbleawsome said:
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.
Click to expand...

That is exact. Answer was
34.9%
. Formula is probability of a and b over probability of b. Or

P(A and B)
P(B)
Click to expand...

wtf

no, just no
 
the problem or the answer, one of the two

let's tweak the numbers for another example

2% chocolate and 50% of chocolates have nuts

so in 100 deserts there is 1 chocolate with nuts and 1 chocolate without nuts and 98 with no chocolate

according to that methodology odds are .02/.5 = 4% that a desert with chocolate will have nuts

in reality the odds remain 50% that a chocolate treat will have nuts

alternatively, the odds that a desert at random will have chocolate and nuts is 1%. there is no way to make 4% make sense
 
tynopik said:
the problem or the answer, one of the two

let's tweak the numbers for another example

2% chocolate and 50% of chocolates have nuts

so in 100 deserts there is 1 chocolate with nuts and 1 chocolate without nuts and 98 with no chocolate

according to that methodology odds are .02/.5 = 4% that a desert with chocolate will have nuts

in reality the odds remain 50% that a chocolate treat will have nuts

alternatively, the odds that a desert at random will have chocolate and nuts is 1%. there is no way to make 4% make sense
Click to expand...

Well...

It says there is an 86% PROBABILITY that a dessert contains chocolate, NOT that 86% of the desserts do contain chocolate.

I believe those 2 things are different (probability vs absolute) but
(1) its been 20 years since my stats class
(2) i've been drinking
and
(3) I just don't care.
 
tynopik said:
the problem or the answer, one of the two

let's tweak the numbers for another example

2% chocolate and 50% of chocolates have nuts

so in 100 deserts there is 1 chocolate with nuts and 1 chocolate without nuts and 98 with no chocolate

according to that methodology odds are .02/.5 = 4% that a desert with chocolate will have nuts

in reality the odds remain 50% that a chocolate treat will have nuts

alternatively, the odds that a desert at random will have chocolate and nuts is 1%. there is no way to make 4% make sense
Click to expand...

There are 100 donuts.

86 of them are chocolate.

30 of those 86 also have nuts, a probability of 30/86.

We want to know the probability of grabbing a chocolate with nuts out of the hundred total.

30/86 = X/100

Solve for X



Edit: I'm distraught that I used donuts instead of salty balls to illustrate my thinking.
 
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The problem is poorly worded... apparently probability people think 'also' and 'and' mean the same thing... when they don't always, in conventional english.
Furthermore, your teacher pulls his questions from the same source as these people...

https://www.google.com/search?q=The...nearest+tenth+of+a+percent.&ie=utf-8&oe=utf-8

it should be "The probability of the dessert containing both chocolate and nuts is 30%."
The 2nd to last sentence could just as easily be" what is the percentage of desserts with nuts at this cafe?"
Parts of the wording were likely intended to trick students and other parts are poorly formulated resulting in accidentally misleading students.

The probability that a dessert containing chocolate also contains nuts is 30%
This should generally as per conventional english mean the dessert is chocolate. The chance of this category aka "chocolate dessert" containing nuts is 30%, therefore if it is given that the dessert is chocolate, there is a 30% chance it also has nuts.
 
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fralexandr said:
The problem is poorly worded... apparently probability people think 'also' and 'and' mean the same thing... when they don't always, in conventional english.
Furthermore, your teacher pulls his questions from the same source as these people...

https://www.google.com/search?q=The...nearest+tenth+of+a+percent.&ie=utf-8&oe=utf-8

it should be "The probability of the dessert containing both chocolate and nuts is 30%."
The 2nd to last sentence could just as easily be" what is the percentage of nuts?" This would benefit the students in the case that the class is a MATH class and not a MATHEMATIC WORD PROBLEM class by not obfuscating the intended math with confusing wording.

The probability that a dessert containing chocolate also contains nuts is 30%
This should generally as per conventional english mean the desert is chocolate. The chance of this category aka "chocolate dessert" containing nuts is 30%, therefore if it is given that the dessert is chocolate, there is a 30% it also has nuts.
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That is literally my test question including the answer choices. I'm rather annoyed I got that question wrong, but I'm not about to bring it up with 4 days left lol
 
Bubbleawsome said:
That is literally my test question including the answer choices. I'm rather annoyed I got that question wrong, but I'm not about to bring it up with 4 days left lol
Click to expand...

have mercy on next year's students and suggest he change the wording of the question in the future
 
The idea isn't to make the word problem obvious, it's to make students think about what is going on.

I don't see any problem with the wording.

"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%."

86% contain chocolate.

30% contain chocolate + nuts.

"Find the probability that a dessert chosen at random contains nuts given that is contains chocolate."

Logically, it can't be 30 out of the 100 (30%) that have nuts. It can only be 30 of the 86 because the problem limits the total number to just the 86 containing chocolate.
 
Humpy said:
We're talking probabilities though, not absolutes.

I was sloppy with some of the wording.
Click to expand...

it makes no difference in this case

there is a world of difference between saying 'the odds of it being chocolate+nuts is 30%' and 'the odds of a chocolate also having nuts is 30%'

they mean completely different things

one is referring to the population of all desserts (30% of 100% = 30%)
the other is referring just to the population of choc desserts (30% of 86% = 25.8%)
 
I'm not sure what you're saying, but rather than continuing to insist you are right, accept that you are wrong and try to figure out why.
 
The way the question is stated, the correct answer is "The odds of a chocolate also having nuts is 30%."

The author of the question may have meant to ask "what are the odds that a random sweet has both chocolate and nuts," but that's not how the question was written. "Given that it contains chocolate" takes all the non-chocolate sweets out of the equation, and we already know that 30% of the chocolates contain nuts.

The question requires zero math to solve, just basic reading comprehension.
 
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Paladin3 said:
The way the question is stated, the correct answer is "The odds of a chocolate also having nuts is 30%."
Click to expand...

exactly

Paladin3 said:
The author of the question may have meant to ask "what are the odds that a random sweet has both chocolate and nuts," but that's not how the question was written.
Click to expand...

actually fralexandr nailed how it was supposed to be

fralexandr said:
it should be "The probability of the dessert containing both chocolate and nuts is 30%."
Click to expand...

then the given question + solution makes sense
 
Humpy said:
The idea isn't to make the word problem obvious, it's to make students think about what is going on.

I don't see any problem with the wording.

"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%."

86% contain chocolate.

30% contain chocolate + nuts.

"Find the probability that a dessert chosen at random contains nuts given that is contains chocolate."

Logically, it can't be 30 out of the 100 (30%) that have nuts. It can only be 30 of the 86 because the problem limits the total number to just the 86 containing chocolate.
Click to expand...

But since the question states "given that it has chocolate" there is no possibility that the chosen sweet is non-chocolate. So we are now working with only the chocolate sweets and 30% of those contain nuts.
 
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"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."

We don't know but let's say there are 100 donuts in a box. 14 are plain, 56 are chocolate, 30 are chocolate and nuts.

If you blindly reach in and grab any one donut there is an 86% chance it will contain chocolate and a 30% chance it will contain chocolate and also nuts.

What is the chance (%) of pulling out a donut with nuts (given) that (it) contains chocolate?

There are only 86 donuts with chocolate. There are 30 with nuts. Your chance is 30 out of 86.

30/86=34.9%

🙂
 
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