bonanova Posted April 18, 2008 Report Share Posted April 18, 2008 This puzzle can be done without pencil and paper. But if you like to doodle, it's allowed. You have two bags. In one bag there are 4 black balls and 4 white balls. In the other, there are 4 black balls and 4 white balls. You take a ball from each of the bags. What are the chances at least one of the balls you drew is black? Quote Link to comment Share on other sites More sharing options...
0 Nikyma Posted April 18, 2008 Report Share Posted April 18, 2008 This puzzle can be done without pencil and paper. But if you like to doodle, it's allowed. You have two bags. In one bag there are 4 black balls and 4 white balls. In the other, there are 4 black balls and 4 white balls. You take a ball from each of the bags. What are the chances at least one of the balls you drew is black? 50/50 Quote Link to comment Share on other sites More sharing options...
0 itachi-san Posted April 18, 2008 Report Share Posted April 18, 2008 3/4 Quote Link to comment Share on other sites More sharing options...
0 grey cells Posted April 18, 2008 Report Share Posted April 18, 2008 could be BB , WW , WB , BW. So 3 out of 4 times , i.e , 75% you can get 1 of the balls as black. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 18, 2008 Report Share Posted April 18, 2008 To get at least one black, assume Bag (A) and Bag (B) BK (A) & WH (B) or BK (A) & BK (B) or WH(A) & BK (B) =(4/8)*(4/8) + (4/8)*(4/8) + (4/8)*(4/8) = 3 * (1/4) = 3/4 the chance is 75% ? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 18, 2008 Report Share Posted April 18, 2008 To get at least one black, assume Bag (A) and Bag (B) BK (A) & WH (B) or BK (A) & BK (B) or WH(A) & BK (B) =(4/8)*(4/8) + (4/8)*(4/8) + (4/8)*(4/8) = 3 * (1/4) = 3/4 the chance is 75% ? There is a 25% chance of white being picked If the OP had said white - would it be 75%? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 18, 2008 Report Share Posted April 18, 2008 This puzzle can be done without pencil and paper. But if you like to doodle, it's allowed. You have two bags. In one bag there are 4 black balls and 4 white balls. In the other, there are 4 black balls and 4 white balls. You take a ball from each of the bags. What are the chances at least one of the balls you drew is black? I think P(one black)=P(WB)+P(BW)+P(BB)=(1/2)(1/2)+(1/2)(1/2)+(1/2)(1/2)=3/4 Quote Link to comment Share on other sites More sharing options...
0 unreality Posted April 18, 2008 Report Share Posted April 18, 2008 So there is a 25% chance of white being picked If the OP had said white - would it be 75%? yes. Because it's "at least one", so the chances aren't 50/50, though the chances are the same for white and black think of it this way: Black - Black White - White White - Black Black - White all of those, except for 1, have a black included. So it's 3/4. White would also be 3/4, if it was asked of white. It's easy once you see that the probability to get all black is 1/4, all white is 1/4, and one of each is 1/2 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 18, 2008 Report Share Posted April 18, 2008 This puzzle can be done without pencil and paper. But if you like to doodle, it's allowed. ... What are the chances at least one of the balls you drew is black? I doodled a black ball on the paper, so the chances I drew a black one is 100%! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 18, 2008 Report Share Posted April 18, 2008 I doodled a black ball on the paper, so the chances I drew a black one is 100%! This has to be the definitive answer. Good job GIJeff. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 18, 2008 Report Share Posted April 18, 2008 I got the same answer as Jeff ... 100%. Of course, I used pencil and paper. If I had done it in my head, I would have gotten 75% like almost everyone else! Quote Link to comment Share on other sites More sharing options...
0 Brandonb Posted April 18, 2008 Report Share Posted April 18, 2008 Chances are 2:4 (1:2) to end up with a black/white pair. 1:4 to end up with a white/white pair. 1:4 to end up with a black/black pair. So the chance of getting at least one black is 3:4, or 75% Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 18, 2008 Report Share Posted April 18, 2008 yes. Because it's "at least one", so the chances aren't 50/50, though the chances are the same for white and black think of it this way: Black - Black White - White White - Black Black - White all of those, except for 1, have a black included. So it's 3/4. White would also be 3/4, if it was asked of white. It's easy once you see that the probability to get all black is 1/4, all white is 1/4, and one of each is 1/2 except for one is black, except for one is white logic says it can't be 75% of the one you want (murphy's law). I'll open the betting and take the odds that you all seem to think a black is gonna be first. But as I will draw first hoping it;s white then I'll have a 75% chance of winning cool and rich in no time I like the doodle answers ***** for GIJeff Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted April 18, 2008 Author Report Share Posted April 18, 2008 I doodled a black ball on the paper, so the chances I drew a black one is 100%! Heh heh ... look again, there's a white ball right next to it. Wait. The paper is white. You can't see it. But it's there. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 18, 2008 Report Share Posted April 18, 2008 Heh heh ... look again, there's a white ball right next to it. Wait. The paper is white. You can't see it. But it's there. but still...at least one of the ones I drew was black Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted April 18, 2008 Author Report Share Posted April 18, 2008 You're absolutely right. And I thought of that as I posted. But my silliness still seemed worth publishing [iMHO] ... When Puzzle Grandmasters are silly they're clever. When others are silly they get warned. Because those are the rules... Quote Link to comment Share on other sites More sharing options...
0 Brandonb Posted April 18, 2008 Report Share Posted April 18, 2008 You're absolutely right. And I thought of that as I posted. But my silliness still seemed worth publishing [iMHO] ... When Puzzle Grandmasters are silly they're clever. When others are silly they get warned. Because those are the rules... hahaha, because he who makes the rules rules. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 19, 2008 Report Share Posted April 19, 2008 yes. Because it's "at least one", so the chances aren't 50/50, though the chances are the same for white and black think of it this way: Black - Black White - White White - Black Black - White all of those, except for 1, have a black included. So it's 3/4. White would also be 3/4, if it was asked of white. It's easy once you see that the probability to get all black is 1/4, all white is 1/4, and one of each is 1/2 Thanks for Unreality for answering on my behalf. Quote Link to comment Share on other sites More sharing options...
Question
bonanova
This puzzle can be done without pencil and paper.
But if you like to doodle, it's allowed.
You have two bags.
In one bag there are 4 black balls and 4 white balls.
In the other, there are 4 black balls and 4 white balls.
You take a ball from each of the bags.
What are the chances at least one of the balls you drew is black?
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