Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have a bag of toys. 10% of the toys are balls. 10% of the toys are blue.

If I draw one toy at random, what're the odds I'll draw a blue ball?

share|improve this question
    
You need to clarify a bit more: e.g., if 10% of the toys are red balls, and 10% of the toys are blue blocks, then you have 0% probability that you'll draw a blue ball. –  amWhy Nov 28 '12 at 15:01
    
Do you mean 10% of the balls are blue or 10% of the toys are? In the letter case, how does ball-ness and blue-ness relate? –  mkl Nov 28 '12 at 15:01
    
10% of the toys are balls. 10% of the toys are blue. I'll edit the question to reflect that. –  D. Patrick Nov 28 '12 at 15:02
    
You need to add whether "blueness" is uniformly distributed across all toys, or my comment still holds. –  amWhy Nov 28 '12 at 15:04
    
I asked this question because I was trying to answer this question: math.stackexchange.com/questions/246621/…. Now I need to figure out how to assign points to the three correct answers to this question. :-/ –  D. Patrick Nov 28 '12 at 17:00

3 Answers 3

up vote 6 down vote accepted

Since it is not entirely clear from the question, I will assume every toy has an equal probability of being blue. So we are assuming the unlikely proposition that no correlation (positive or otherwise) exists between color and type-of-toy. Otherwise, could very well be that 10% of the toys are neon-green balls (tennis balls, e.g.) and 10% of the toys are blue blocks, in which case you have 0% probability that you'll draw a blue ball.

We know $10$% $ = 0.1$ of the toys are balls, and $10$% $= 0.1$ of these balls are blue.

Then $10$% of ($10$%) of the toys are blue balls.

So the probability of drawing a blue ball is $0.1 \times 0.1 = 0.01$.

This equates to a $0.01 \times 100$% = $1$% probability of drawing a blue ball.


share|improve this answer

Assuming that the balls are not any more or less likely to be blue that other toys, the object drawn has a $.1$ chance of being a ball and a $.1$ chance of being blue. So the chance of it being a blue ball is $.01$.

share|improve this answer

If the "blueness" is uniformly distributed. We have S Toys

From wich $0.1 \mathbf S$ are Balls.
$P(X)= \frac {0.1S}S=0.1$

$0,1 \mathbf S$ are Blue toys.
$P(Y)=\frac {0.1S}S=0.1$

If you want Blue ball you have
$P(XY)=P(X)\cdot P(Y) = 0.1 \times 0.1 = 0.01 = 1 $%

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.