Dispute with friend.

Steven G

Steven G

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A box contains 5 strawberry candies, 3 banana candies, and 2 orange candies. If Braden selects 2 candies at random from this box, without replacement, what is the probability that both candies are not banana?

I claim that this allows one candy to be a banana, no friend claims that no candy can be a banana.
Who is correct?
 
Use hypergeometric distribution:
N: Population Size = 10
k: Number considered as success in the population = 7 (not banana)
n: Number of trials = 2
x: Number considered as success = 2 ( two picks that are not banana)
[math]h(2;10,7,2) = \frac{{7 \choose 2}{3\choose 0}}{10 \choose 2} \approx 47\%[/math]
 
Jomo said:
A box contains 5 strawberry candies, 3 banana candies, and 2 orange candies. If Braden selects 2 candies at random from this box, without replacement, what is the probability that both candies are not banana?

I claim that this allows one candy to be a banana, no friend claims that no candy can be a banana.
Who is correct?
Click to expand...

This is an English-language problem -- and by that I mean, it's a problem with the English language, which does not have a clear "order of operations".

"Both candies are not banana" might mean either "It is not true that both candies are banana" or "Both candies are non-banana". In my ears, the latter sounds more natural (the way most humans might interpret it), but the former sounds more formally correct (the way mathematicians or logicians at their worst might interpret it).

The author of the problem is wrong. You're both right (unless you wrote the problem).
 
Jomo said:
A box contains 5 strawberry candies, 3 banana candies, and 2 orange candies. If Braden selects 2 candies at random from this box, without replacement, what is the probability that both candies are not banana?

I claim that this allows one candy to be a banana, no friend claims that no candy can be a banana.
Who is correct?
Click to expand...

Jomo, the question is wrong to begin with in more than one way. Neither of you is
right, because the problem makes no sense. Each of the above candies should be
referred to as strawberry-flavored, banana-flavored, or orange-flavored, as the case
may be. They question cannot logically switch a banana candy, supposedly made
from a banana, to an actual banana.
 
Last edited:
lookagain said:
They question cannot logically switch a banana candy, supposedly made
from a banana, to an actual banana.
Click to expand...

This site has been freezing me out this afternoon to make edits in a timely manner.

* "The question cannot logically switch from a banana candy, supposedly made from a banana, to an actual banana."
 
I did not write the problem.
I too thought that we werre both correct.
My friend just needed written proof that we are both correct.
 
Jomo said:
A box contains 5 strawberry candies, 3 banana candies, and 2 orange candies. If Braden selects 2 candies at random from this box, without replacement, what is the probability that both candies are not banana?\
Click to expand...
This entire thread reminds me of my favorite anecdote. First, I urge any one to carefully read replies #3 & 4.
This comes from Mathematical Apocrypha by Steve Krantz. In the early part of the last centenary there was quite a battle for priory among the centers of mathematics higher education. The great E. H. Moore was at Chicago, a relatively new school and S. Lefschetz was at Princeton..Moore was invited to lecture at Princeton. Moore began his lecture by saying “Let a be a point and let b be a point.” Lefschetz shouted out “But why don't you just say “Let a and b be points?” Moore replied “Because a may equal b.” Lefschetz stormed out of the room.
 
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