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How do you divide the marbles up so that you have the greatest probability of choosing a white marble?

I'm not sure if it's been posted before but I liked it...

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- #1

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How do you divide the marbles up so that you have the greatest probability of choosing a white marble?

I'm not sure if it's been posted before but I liked it...

- #2

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I assume this is meant to simply mix the bowls up, and not the marbles? That is, the marbles will not be moved from one bowl to the other-- merely have their positions in their already-assigned-bowls moved around so that (for example) one at the top might wind up somewhere in the middle, and so forth.Then I will blindfold you and mix the bowls and marbles up.

I get a 74.747474... percent chance of living...

DaveE

- #3

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yeah.I assume this is meant to simply mix the bowls up, and not the marbles? That is, the marbles will not be moved from one bowl to the other-- merely have their positions in their already-assigned-bowls moved around so that (for example) one at the top might wind up somewhere in the middle, and so forth.

I get a 74.747474... percent chance of living...

DaveE

how did you arrange the marbles. (its right by the way)

- #4

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I get 98% minimum.

Put one white marble in one of the bowls and leave the rest in the other.

- #5

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I'm pretty sure that would give you 74.74747474% chance of survival. It's 50/50 (so equal) that you choose one or the other bowl. If you pick one bowl you have 100% chance of survival. If you choose the other bowl you have 49/99 so basiaclly 49.494949% Since both have equal probability of occuring you add them and divide by total amount of percentage (so 200%)I get 98% minimum.

Put one white marble in one of the bowls and leave the rest in the other.

100%+49.4949...%=149.4949...%

149.4949.../200= 74.7474...% chance of survival. It's completely possible however my math is totally wrong. How did you end up with 98%?

- #6

Matterwave

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I get 100%

Put one white marble in one, all the rest in the other. Blindfolded, pick the bowl that only has 1 marble in it... <_<

If you're not allowed to feel around, then I'm not sure atm.

- #7

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The math is correct, although I don't think it's quite how one would typically express the probability (as in, the way probability is taught-- I could be wrong, I'm not sure. It's been a while since my last class on the subject). The 4 outcomes would be:It's completely possible however my math is totally wrong.

A) Pick a white marble from bowl 1

B) Pick a black marble from bowl 1

C) Pick a white marble from bowl 2

D) Pick a black markble from bolw 2

So, to start with, there's a 1/2 chance of picking bowl 1. Then, assuming that bowl 1 has a single white marble, there's a 1/1 chance of picking a white marble, and a 0/1 chance of picking a black marble.

Next, there's a 1/2 chance of picking bowl 2. And a 49/99 chance of picking a white marble from bowl 2, with a 50/99 chance of picking a black marble from bowl 2.

Hence:

A) 1/2 * 1/1 = 0.5

B) 1/2 * 0/1 = 0.0

C) 1/2 * 49/99 ~ 0.24747474...

D) 1/2 * 50/99 ~ 0.25252525...

The overall chance of picking a white marble

= A+C

= 1/2 * 1/1 + 1/2 * 49/99

~ 0.5 + 0.24747474...

~ 0.74747474...

Or, the alternate way (often easier in probability problems) is to realize that there's only 1 viable way of picking a black marble, which is to pick it from bowl 2. Hence, you can just state:

Overall chance of picking a white marble

= 1 - chance of picking a black marble

= 1 - 1/2 * 50/99

~ 1 - 0.25252525...

~ 0.74747474...

DaveE

- #8

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Ah thanks daveE, I only did it that way though because I already knew that both bowls were on equal footing. Your way is correct though.

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Why would you average the probabilities together?I'm pretty sure that would give you 74.74747474% chance of survival. It's 50/50 (so equal) that you choose one or the other bowl. If you pick one bowl you have 100% chance of survival. If you choose the other bowl you have 49/99 so basiaclly 49.494949% Since both have equal probability of occuring you add them and divide by total amount of percentage (so 200%)

100%+49.4949...%=149.4949...%

149.4949.../200= 74.7474...% chance of survival. It's completely possible however my math is totally wrong. How did you end up with 98%?

But, yes, daveE is right. I just noticed that I did the math wrong -_- it should be 74.74%

- #10

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Because they are on even footing (since it's 50/50)? It's definitely not wrong. Why would I want to waste my time figuring out what the percentage value out of 100% is and then figure the percentage of 50% that represents and then add them when I could just do it all at once?Why would you average the probabilities together?

- #11

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I'm with you on this one. There's nothing in the instructions which say they have to be divided equally, or that you're not allowed to reach for the bowls and pick the marble out yourself.

Put one white marble in one, all the rest in the other. Blindfolded, pick the bowl that only has 1 marble in it... <_<

If you're not allowed to feel around, then I'm not sure atm.