Simple Probability

[mcdoughboy]

I'm having a hard time grasping my mind around this question:

"Urn A has 5 white and 8 red balls. Urn B has 11 white and 17 red balls. We flip a fair coin. If the oucome is heads, then a ball from urn A is selected, whereas if the oucome is tails, then a ball from urn B is selected. Suppose that a white ball is selected. What is the probability that the coin landed heads?"

Shouldn't the probability the coin landed heads ALWAYS be 1/2, no matter what the following outcome is? I feel as though it's not because a white ball was selected from urn A that it is more or less likely that you drew heads. I asked my professor about this and here's his response "Suppose that a white ball is selected..." As you can see he was very mysterious about it, and that does not help.

Thanks!

 

[tkhunny]

If we are thinking only of coin flipping, yes, 1/2 every time. That is not the question.

Heads: 5 to 8
Tails: 11 to 17

P(Heads) = 1/2
P(Tails) = 1/2

P(White|Heads) = 5/13
P(White|Tails) = 11/28

P(White) = (1/2)(5/13) + (1/2)(11/28)
P(Red) = (1/2)(8/13) + (1/2)(17/28)

Your challenge is to find P(Heads|White). Can you say, "Bayes Theorem"?

 

[mcdoughboy]

Woo I got it I was thinking of conditional probability and not the theorem itself.
Thanks a lot!