Conditional Probability, Independence & Bayes · Challenge problem

Urn I contains $3$ red balls and $1$ blue ball; urn II contains $1$ red ball and $3$ blue balls. One urn is chosen by a fair coin toss, and then $4$ balls are drawn from it one at a time with replacement. The draws come out red, red, blue, red. What is the probability that urn I was chosen? Express your answer as a common fraction.