SOLUTION: An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both

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Question 269858: An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same colour is 0.44. Calculate the number of blue balls in the second urn.
Found 3 solutions by drk, ptaylor, Edwin McCravy:
Answer by drk(1908) About Me  (Show Source):
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Probability same color means 2 red or 2 blue
P(red from both) = (4/10) * 16/(16+b)
P(blue from both) = (6/10) * b/(16+b)
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The sum of these = .44 so we can say
(i) 4%2F10%29+%2A+%2816%2F%2816%2Bb%29%29+%2B+%286%2F10%29+%2A+%28b%2F%2816%2Bb%29%29+=+.44
combining like terms, we get
(ii) %2864+%2B+6b%29%2F%2810%2A%2816%2Bb%29%29+=+.44
cross multiply to get
(iii) 64+%2B+6b+=+4.4%2816+%2B+b%29
distribute to get
(iv) 64+%2B+6b+=+70.4+%2B+4.4b
subtract 64 and then subtract 4.4b to get
(v) 1.6b+=+6.4
divide to get
b+=+4

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=number of blue balls in the 2nd urn
Total number of balls in 2nd urn is (16+x)
P1---Probability of drawing a blue ball in first urn is 6/10
P2---Probability of drawing a blue ball in 2nd urn is x/(16+x)
Probability of P1 and P2 occurring together is P1*P2, so:
(6/10)(x/(16+x)=44/100 and this equals
6x/10(16+x)=44/100 multiply each side by 100(16+x)
60x=44(16+x) or
60x=704+44x
16x=704
x=44---------------number of blue balls in 2nd urn
CK
(6/10)(44/60)=44/100
44/100 = 44/100
Does this help??---ptaylor

Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same colour is 0.44. Calculate the number of blue balls in the second urn.

Suppose there are N blue balls.

Then 

P(Red from first urn) = 4%2F10+=+2%2F5
P(Red from second urn) = 16%2F%2816%2BN%29

P(Red from 1st Urn AND Red from 2nd Urn) = %282%2F5%29%2816%2F%2816%2BN%29%29

P(Blue from first urn) = 6%2F10+=+3%2F5
P(Blue from second urn) = N%2F%2816%2BN%29

P(Red from 1st Urn AND Red from 2nd Urn) = %282%2F5%29%2816%2F%2816%2BN%29%29=+32%2F%285%2816%2BN%29%29
P(Blue from 1st Urn AND Blue from 2nd Urn) = %283%2F5%29%28N%2F%2816%2BN%29%29=%283N%29%2F%285%2816%2BN%29%29

P(Same color) = 

P[(Red from 1st Urn AND Red from 2nd Urn) OR (Blue from 1st Urn AND Blue from 2nd Urn)] = 

P(Red from 1st Urn AND Red from 2nd Urn) + P(Blue from 1st Urn AND Blue from 2nd Urn)] =



We are told this equals 0.44=44%2F100=11%2F25

%2832%2B3N%29%2F%285%2816%2BN%29%29+=+11%2F25

Can you solve that equation for N?  If not post again asking
how to solve it.

Answer N=4.  So there are 4 blue balls.

Edwin