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.
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Suppose there are N blue balls.

Then 

P(Red from first urn) = {{{4/10 = 2/5}}}
P(Red from second urn) = {{{16/(16+N)}}}

P(Red from 1st Urn AND Red from 2nd Urn) = {{{(2/5)(16/(16+N))}}}

P(Blue from first urn) = {{{6/10 = 3/5}}}
P(Blue from second urn) = {{{N/(16+N)}}}

P(Red from 1st Urn AND Red from 2nd Urn) = {{{(2/5)(16/(16+N))= 32/(5(16+N))}}}
P(Blue from 1st Urn AND Blue from 2nd Urn) = {{{(3/5)(N/(16+N))=(3N)/(5(16+N))}}}

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)] =

{{{32/(5(16+N))+ (3N)/(5(16+N)) = (32+3N)/(5(16+N))}}}

We are told this equals {{{0.44=44/100=11/25}}}

{{{(32+3N)/(5(16+N)) = 11/25}}}

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</pre>