1. ## Probability

Hi everyone,

I really need an urgent help with the task below!!!

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.

2. $\displaystyle \frac{6}{10}\cdot \frac{b}{(16+b)} + \frac{4}{10}\cdot \frac{16}{(16+b)} = 0.44$
Solve for b.

3. Originally Posted by kochwow
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.
Let N be the number of blue balls in the second urn. The probability that the first ball drawn is red is 2/5. The probability that the second ball is also red is 16/(16+N) so the probability both balls are red is (2/5)(16/(16+N)).

The probability that the first ball is blue is 3/5 and the probability that the second ball is blue is N/(16+N) so the probability that both balls are blue is (3/5)(N/(16+N)).

The probability that the two balls are the same, then, is (2/5)(16/(16+N))+ (3/5)(N/(16+N)). To find N, solve (2/5)(16/(16+N))+ (3/5)(N/(16+N))= 0.44 for N.