an unfair coin with Pr[H]=0.3 is flipped.

Question

an unfair coin with Pr[H]=0.3 is flipped. if the flip results in a head, a marble is selected at random from a urn containing two red and eight blue marbles. otherwise a marble is selected from a different urn containing three red and five blue marbles. of the selected marble is red, what is the probability that the flip resulted in a head?

Answer 1

Prob(Head|red) = Prob(red|head)*prob(head)/prob(red)

prob(red) = 0.3*0.2+ 0.8*0.375 = 0.36

= 0.2 * 0.3 / 0.36

= 0.16 = 1/6