An unfair coin with Pr[H] = 0.2 is flipped. If the flip results in a head, a marble is selected at random from a urn containing four red and six blue marbles. Otherwise, a marble is selected from a different urn containing one red and seven blue marbles. If the selected marble selected is red, what is the probability that the flip resulted in a head? If necessary, round your answer to 4 decimal places.

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