by Whitebunny
Tags: hard, probability
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,706 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.
P: 2
 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...

HW Helper
P: 4,504

Try to do it systematically. Let's look at the contents of the urn *after* the first event.
$$\begin{array}{ccc} \text{first event}&\text{probability} & \text{new contents}\\ \hline \text{red} & 1/2 & \text{5 red, 5 blue}\\ \text{blue,heads} & 1/4 &\text{5 red, 4 blue}\\ \text{blue,tails}& 1/4 & \text{5 red, 6 blue} \end{array}$$
So, before drawing the second ball the urn has either 5 red and 5 blue, or 5 red and 4 blue, or 5 red and 6 blue, and you have probabilities of each. Now you can look at what happens after drawing the second ball, etc., etc. Essentially, there will always be 5 red balls, so you can just look at the number of blue balls at each stage. If you have studied Markov chains, this would be an obvious example; if not, you can just do it manually. It really is not too bad: you are asked to find the probability that all three balls drawn are the came color. So the drawings are either RRR or BBB. Getting P{RRR} should be easy. Getting P{BBB} needs a bit more work, along the lines of what I showed above. In getting P{BBB} the color is always blue, so the only factors you need worry about are the first two coin-toss results; you should ask yourself whether HT and TH would each give the same answer.

RGV

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