Brain Teasers
Colorful Odds
Fun: (2.29)
Difficulty: (1.84)
Puzzle ID: #18301
Submitted By: wizecracker55 Corrected By: Winner4600
Submitted By: wizecracker55 Corrected By: Winner4600
Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.Probability
There are four colored balls in a hat: two red, one black and one blue. After pulling out two of them, you know that one of them is red, but you do not know which one. What is the probability that both balls are red?
Answer
1 in 5. The only possible combinations are:[1] red1, black
[2] red1, blue
[3] red1, red2
[4] red2, black
[5] red2, blue
[6] black, blue
Since you know that one of the balls is red, that eliminates possibility [6], which has no red. Therefore, because all the remaining possibilities are equally likely, the probability is 1/5.
Hide Answer Show Answer
What Next?
View a Similar Brain Teaser...
If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.
Solve a Puzzle
Comments
I agree with the answer but...
I'm just going to wait for somebody to challenge the answer.
I'm just going to wait for somebody to challenge the answer.
I found this not fun because i dont like math
Then what are you doing looking at probability teasers? Probability involves math.
Good puzzle. The answer is correct provided you didn't look at the two you pulled out. Say you held them behind your back and someone else looked and said "At least one of them is red". That is OK because you don't know which one is red. But say you peeked at one and saw it was red. Then you would know that it was R1 (or R2). It doesn't matter what you call it but you would know that one particular ball was red. The question would now be "What is the probability that the other particular ball is also red" Now the answer would be 1 in 3 as the unseen ball is either the other red, the blue or the black.
Jimbo is correct - the answer is 1 in 5 if you don't know the color of either ball. Since you know one is red the odds are 1 in three that the other is also red
We don't know the color of either ball, harpoon - only that one of them is red. We don't know which one is red or even which of the two red balls it is.
I have to agree with jimbo and harpoon, if you KNOW that one ball is red, and are calculating the probability that the "other" one is red, then you don't need to know which ball is which. The "other" ball is either the black, blue or (second) red ball so the probability is 1 in 3.
Now that I think about it, and look back at the teaser Dogs, the answer would be correct if you say, "At least one is red, what are the odds of both being red?" In this case, it explicitly says, "One is red, what are the odds of the other being red?" In this case, the answer would indeed be 1/3. I step down from my position and step up on the other, and if anyone wants to take my place as the defendant of the answer, go right ahead.
Perhaps the wording of the teaser is a bit ambiguous. It says 'After pulling out two of them, you know that one is red.' when it should say 'after pulling out two of them, you know that one of them is red'. The wording, while not directly adressing it, might seem to suggest that you know which ball is red and which is not, when in fact you do not. You know that ONE OF the balls is red, but you have no idea which one. In this case, the answer of 1:5 holds true, as there are 5 possible combinations including at least one red, and only one which affords for both being red.
If you meant to put that you don't know which is which, then get someone to edit your teaser to say, "You know at least one is red. What are the odds of both being red?" That way your answer, although it with all likelihood will still be attacked, will have the benefit of being right.
Much better.
The odds are NOT 1:5. the odds are 1:4. Odds are defined as the probability of success divided by the probability of failure. (1/5)/(4/5) = 1/4 or 1:4 odds
The probability is 1/5, though, you'll agree? Perhaps he merely inserted the wrong symbol. In that case, then this teaser must be edited again.
I just wish to point out something. The combinations mentioned are:
[1] red1, black
[2] red1, blue
[3] red1, red2
[4] red2, black
[5] red2, blue
[6] black, blue
There is one more combination that you guys has missed out.
[7]red2, red1
hence the possibility should be 1/6.
odds are calculated by the number of success over the total possible outcome. 2/4 x 1/3 = 1/6
2/4 because there are 2 red balls and 4 possible balls to choose from. 1/3 is because there is only one red ball left and total of 3 balls to choose from.
ianicx, you're wrong as the selections are not ordered: we don't care which ball came out first. If you included red2, red1 as well as red1, red2, then you need black,red1, blue,red1, etc.
EZ!!!!!!!!!!
If you pull out 2 balls, how would you know one of them is red? The answer states that there is a combination where the balls are black and blue (Combination 6). Therefor, you might not pick a red one out at all.
Cool teaser! I got the answer wrong!
good 1
Jul 12, 2005
still confused on what is the right answer, so i tested it, and out of 100 test tries where at least 1 was red i came up with 17 times where both were red. Not definetive, yet im leaning to the 1 in 5 even though it still dont make sense to me.
quite confusing
Sep 28, 2005
You know that one of them is red. Is that still probability? I think that should be the question to discuss.
probability
For an experiment, the total number of successful events divided by the total number of possible events.
Is the total number of possible events changed once your possibilities are limited or once you know something. Once something is certain, does probability still apply or is there still a variable that makes things uncertain?
probability
For an experiment, the total number of successful events divided by the total number of possible events.
Is the total number of possible events changed once your possibilities are limited or once you know something. Once something is certain, does probability still apply or is there still a variable that makes things uncertain?
Sep 28, 2005
You know that one of them is red. Is that still probability? I think that should be the question to discuss.
probability
For an experiment, the total number of successful events divided by the total number of possible events.
Is the total number of possible events changed once your possibilities are limited or once you know something. Once something is certain, does probability still apply or is there still a variable that makes things uncertain?
probability
For an experiment, the total number of successful events divided by the total number of possible events.
Is the total number of possible events changed once your possibilities are limited or once you know something. Once something is certain, does probability still apply or is there still a variable that makes things uncertain?
Jan 21, 2006
The confusion over this teaser is pointed out in "Odds Oddities" the fact that one red ball has been selected has no effect on the odds of two red balls being the outcome, it only eliminates the possibility that the outcome is blue/black -- one possibility out of six.
i get 1/3. Just assume that there is only one red ball, one black, and one blue (because one ball has already taken and you know that the ball is red). the probability a red ball is taken is 1/3. So, the answer is 1/3
If you want to define red1/black and red2/black as two possible outcomes, then you must allow for red1/red2 and red2/red1 to exist as two outcomes also. After eliminating black/blue we are left with 6 equally probable events, 2 of which fit our criteria. Probability is 1/3. Sorry to revisit such an old puzzle but I'm new here and noticed that this point hadn't been made.
This is similar to many of the other puzzles. The question is ambiguous because we don't know how we learned one ball is red.
If the auditor was asked, "is at least one of the two balls red?" and he answered, "yes", then your 1/5 answer is correct.
If on the other hand, we asked the auditor to randomly chose one of the two balls and disclose it's color and he reported, "red", then the answer is 1/3.
If the auditor was asked, "is at least one of the two balls red?" and he answered, "yes", then your 1/5 answer is correct.
If on the other hand, we asked the auditor to randomly chose one of the two balls and disclose it's color and he reported, "red", then the answer is 1/3.
I CHALLENGE THE ANSWER!!!!
it would be a 1/3 chance. one case was not shown and that is if you pull red2 then red1 then it would be 2/6 odds which is equal to 1/3
i fell smart now
it would be a 1/3 chance. one case was not shown and that is if you pull red2 then red1 then it would be 2/6 odds which is equal to 1/3
i fell smart now
To post a comment, please create an account and sign in.
Follow Braingle!