I have two dices. One has 6 sides and one have 8 sides.
I select which one to roll based on a flip of a fair coin.
A dice it's selected based on whether the flip of this coin. If it's head, the 6-sided dice it's rolled, 8-sided otherwise.
What's the probability of that coin flip was heads given the roll was 5?
I'm trying to solve using bayes rule here.
I think it'll be:
P(HEADS|5) = [P(5|HEADS)*P(HEADS)] / P(5)
I'm trying with:
P(5|HEADS) = 1/6 P(HEADS) = 1/2 P(5) = 2/14
Which results in: 0.58356676
But it's not the correct answer.
I think I'm confusing the value that it's supposed to be in P(5|HEADS).