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## Question

Moe and May went to the beach the other day.

While May was setting out food for the picnic, Moe collected a bagful of pretty stones.

When he returned, he spread them out on the cloth for Mae to see.

Take as many of them as you like, he said, and put them in your bag.

While you finish preparing the food I'll fill my bag with more stones.

When they returned home, they counted their stones.

What is the probability they had an even number of stones between them? 

Edited by bonanova
clarify - total number of stones is even

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They both had an even number or the total of both of them was even?

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They both had an even number or the total of both of them was even?

Total.

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Moe and May went to the beach the other day.

While May was setting out food for the picnic, Moe collected a bagful of pretty stones.

When he returned, he spread them out on the cloth for Mae to see.

Take as many of them as you like, he said, and put them in your bag.

While you finish preparing the food I'll fill my bag with more stones.

When they returned home, they counted their stones.

What is the probability they had an even number of stones?

Assuming that you are referring to the total number they have between the two of them:

2 in 3

even + odd = odd

odd + odd = even

even + even = even

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What is the probability they had an even number of stones between them? 
the odds are even
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Moe and May went to the beach the other day.

While May was setting out food for the picnic, Moe collected a bagful of pretty stones.

When he returned, he spread them out on the cloth for Mae to see.

Take as many of them as you like, he said, and put them in your bag.

While you finish preparing the food I'll fill my bag with more stones.

When they returned home, they counted their stones.

What is the probability they had an even number of stones between them? 

50% A&B both even, A&B both odd, A-even B-odd, A-odd B-even : 2 of these give odd total and 2 give even total

Edited by HokieKen
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You're saying he fill up the bag twice, does "filling it up" mean that he will have the same amount of stones in his bag the first fill as he does the second fill?

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1/2?

May's stones + Moe's stones =total
1) odd + odd = even
2) odd + even = odd
3) even + even = even
4) even + odd = odd
`   `

probablilty of even = 2/4 = 1/2

or perhaps i'm missing something here.....

so i agree with d3k3 and HokieKen

Edited by lemonymelon
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You're saying he fill up the bag twice, does "filling it up" mean that he will have the same amount of stones in his bag the first fill as he does the second fill?

Assumptions are important.

1. Assume Moe filled his bag both times - before and after Mae took some from his first bagful.
2. Assume the stones are of various sizes.
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Moe and May went to the beach the other day.

While May was setting out food for the picnic, Moe collected a bagful of pretty stones.

When he returned, he spread them out on the cloth for Mae to see.

Take as many of them as you like, he said, and put them in your bag.

While you finish preparing the food I'll fill my bag with more stones.

When they returned home, they counted their stones.

What is the probability they had an even number of stones between them? 

virtually 50-50 but...

Slightly more likely to be odd, since odd goes first then even catches up. The more stones they collect, the smaller this difference is.

Or am I on crack?

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I know!!!

are both OCD and will only pick up 2 stones at a time. So there is 100% chance that they have and even #.

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virtually 50-50 but...

Slightly more likely to be odd, since odd goes first then even catches up. The more stones they collect, the smaller this difference is.

Or am I on crack?

OK, you've raised the final point. So let's expand our list of assumptions.

1. Assume Moe filled his bag both times - before and after Mae took some from his first bagful.
2. Assume the stones are of various sizes.
3. Assume when Moe fills his bag, both times, it's equally likely that the bag contains an even or an odd number of stones.
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OK, you've raised the final point. So let's expand our list of assumptions.
1. Assume Moe filled his bag both times - before and after Mae took some from his first bagful.
2. Assume the stones are of various sizes.
3. Assume when Moe fills his bag, both times, it's equally likely that the bag contains an even or an odd number of stones.

Any way I cut it I come back to 50%. Three 50/50 shots at even/odd is still 50/50. If you have 2x+y (this would assume the rocks he picked up were equal to the rocks Mae took) where x could be either even or odd, and y could be either even or odd, it's still 50/50.

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OK, you've raised the final point. So let's expand our list of assumptions.
1. Assume Moe filled his bag both times - before and after Mae took some from his first bagful.
2. Assume the stones are of various sizes.
3. Assume when Moe fills his bag, both times, it's equally likely that the bag contains an even or an odd number of stones.

i get

50-50 no matter how I figure it. Have 3 variables with 2 possible values. Mo's first fill, Mo's second fill, and Mae's fill. This is 2^3 possible combinations. Of the 8 possible, 4 result in even totals and 4 result in odd totals. What am I missing?

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Since May had to bring the materials for the picnic she could not have carried as many stones as may.

However, even though the quantity between the two is different, there is 0 indication regarding the numerical quantity.

Therfore it's 50/50.

Is this cumulative even or individual even ?

It might be 25%

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Just re-read the question. I was under the impression Moe went back to fill up his bag after May had selected the rocks and he had put the rest back into his bag. Re-reading, it seems he left the rocks on the cloth while he went to re-fill his bag.

Since his bag was already full upon his second return, all rocks that May did not pick up must have been discarded, or May must have picked up all of the rocks.

There was a 50% chance that Moe picked up even rocks on his first fill.

There was a 50% chance that Moe picked up odd rocks on his first fill.

If Moe picked up an even amount of rocks, there was a 50% chance May took an even amount of rocks.

If Moe picked up an odd amount of rocks, there is a lower than 50% chance that May took an even amount of rocks because there is always 1 more odd number than even in an odd-lengthed array of numbers. For example, 1 2 3 4 5 contains 3 odds and 2 evens.

There was another 50% chance that Moe picked up even rocks on his second fill.

There was another 50% chance that Moe picked up odd rocks on his second fill.

I don't think there is a definite percentage because if he picked up 301 rocks the chance of picking an even amount(49.8%) would be higher than if he picked up 3 rocks. (33%)

The absolute lowest possible odd amount would be 3 rocks (Because you state he picks up multiple rocks, not just 1)

So the answer would have to be 33% < probability < 50%.

Edited by Llam4
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HokieKen, was your spoiler a request?

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I edited my previous post inside the spoiler tags, with a guess.

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I edited my previous post inside the spoiler tags, with a guess.

Bingo.

Nice going.

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Just re-read the question. I was under the impression Moe went back to fill up his bag after May had selected the rocks and he had put the rest back into his bag. Re-reading, it seems he left the rocks on the cloth while he went to re-fill his bag.

Assume Moe collected the rocks Mae did not take and he then finished filling his bag [the 2nd time] from the beach.

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HokieKen, was your spoiler a request?

It was, but Llam has shown me the error of my ways. Now another possible wrench in the works.... the stones that Mae left laying on the blanket when she put some in her bag, did those stones get folded up in the blanket and go home with them or did they get left behind.

And to Llam's logic...

It is stated that there is one more odd # in any given string than even. But if we discard the #1 as a possibility because stones is plural, it evens out. So wouldn't the odds even out as well?

My brain hurts

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It is stated that there is one more odd # in any given string than even. But if we discard the #1 as a possibility because stones is plural, it evens out. So wouldn't the odds even out as well?

The fact is that he PICKED UP more than 1 stone. May may have only taken one stone, nowhere was it stated that she picked up more than one. So say he picked up 7 stones, she could possibly pick up: 1, 2, 3, 4, 5, 6, or 7 stones. There's a 3/7 chance it's even, a 4/7 chance it's odd.

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The fact is that he PICKED UP more than 1 stone. May may have only taken one stone, nowhere was it stated that she picked up more than one. So say he picked up 7 stones, she could possibly pick up: 1, 2, 3, 4, 5, 6, or 7 stones. There's a 3/7 chance it's even, a 4/7 chance it's odd.

Correct you are

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So is the conclusion that there is no definitive answer, only a range Bonanova?

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So is the conclusion that there is no definitive answer, only a range Bonanova?
the odds are even. npi.
they are not even, slightly favoring odd [May's bag].

Moe's bag is 50-50 by assumption.

you knew the odd number of stones Moe initially filled his bag with,

the 50% of the time his bag initially had an odd number of stones.

That's the only thing the odds depend on.

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You didn't know the answer before you posted this did you? Are you a politician?

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