9. A gambler has two dice, an unbiased one, and a loaded one which, when tossed, lands on 6 with probability of 4/9 and lands on any of the other faces with probability of 1/9.

The gambler does not know which die is the loaded one. He chooses one of the two dice at random and tosses that die ten times in a row. If it lands on 6 exactly four times, what is the probability that it is the loaded one?