Bob has two six sided dice. One of dice is fair, but the other is biased as well as shows one of the its faces with probability 1/2 and each of its other faces with the probability of 1/10. Alice picks oneof Bob's dice at random and rolls its 10 times. She notes that the number 4 appears exactly 3 times among the 10 rolls.
a. Is it more likely that Alice picked the fair die or the biased one?
b. Would you change your answer if it is known that Bob's biased die has probability 1/2 of rolling a 4?