1. The problem statement, all variables and given/known data
Ten balls are in an urn; five red and five blue. When a red ball is removed, it is always
replaced. When a blue ball is removed a coin is flipped. If heads appears the ball is not
replaced. If tails appears, then two blue ones are placed into the urn. What is the
probability that the first three balls drawn are the same color?

2. Relevant equations
I honestly have no idea. Very sorry.

3. The attempt at a solution
Draw 1
Red 50% chance, Blue 50% (heads 50%, tails 50%)

Draw 2 (this is where I get confused)
if first draw red then, Red 50% chance, Blue 50% (heads 50%, tails 50%)
if first draw blue and tails then, Red 5/11, blue 6/11 (heads 50%, tails 50%)
If first draw blue and heads then, Red 5/9, blue 4/9 (heads 50%, tails 50%)

Draw 3
if first draw red, if second draw red then, Red 50% chance, Blue 50%
if first draw red then, and second draw is blue and tails then, Red 5/11, Blue 6/11
If first draw red, and second draw is blue and heads then, Red 5/9, Blue 4/9
If first draw is blue and tails, and second draw is red, then Red 5/11, Blue 6/11
If first draw is blue and tails, and second draw is blue and tails, then Red 5/12, Blue 7/12
If first draw is blue and tails, and second draw is blue and heads, the Red 50% chance, Blue 50%
If first draw is blue and heads, and second draw is red, then Red 5/9, Blue 4/9
If first draw is blue and heads, and second draw is blue and tails then, the Red 50% chance, Blue 50%
If the first draw is blue and heads, and the second draw is blue and heads, then Red 5/8 chance, Blue 3/8
Then I multiply everything together (?)
.5*.5*.5*.5*5/11*6/11*5/9*4/9*.5*.5*5/11*6/11*5/9*4/9*5/12*7/12*.5*.5*5/9*4/9*.5*.5*5/8*3/8
=itty bitty number that can’t possible be the answer.

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 Recognitions: Gold Member Science Advisor Staff Emeritus Set up a tree: R B / \ / \ R B R B / \ / \ / \ / \ R B R B R B R B Calculate the probability, step by step, of each of those 8 outcomes.

 Quote by HallsofIvy Set up a tree: R B / \ / \ R B R B / \ / \ / \ / \ R B R B R B R B Calculate the probability, step by step, of each of those 8 outcomes.
Are you sure this works here? Because of the coin flipping and removal, shouldn't there be more possible outcomes? Could you please elaborate a bit more? I really don't understand...

Recognitions:
Homework Help

$$\begin{array}{ccc} \text{first event}&\text{probability} & \text{new contents}\\ \hline \text{red} & 1/2 & \text{5 red, 5 blue}\\ \text{blue,heads} & 1/4 &\text{5 red, 4 blue}\\ \text{blue,tails}& 1/4 & \text{5 red, 6 blue} \end{array}$$