Little John is very fond of candies; he always has a few in his pockets. Not sure about his HW favorite flavor, he proceeds with a game to choose them. In his left pocket, he puts 5 orange and 3 strawberry candies, and in the right, he puts 4 orange and 2 strawberry. He then draws a coin and if it lands on tails, he draws a candy from the left pocket, and if it lands on heads,

he picks one from his right pocket. The coin is of course perfectly balanced.

(a) What is the probability that after two flips, he ended up eating two candies with the same flavor?

(b) He gets back home and empties his pockets on the table. His mother, aware of his game, finds 7 orange candies and 5 strawberry candies. Help her figure out the sequence of the two coin flips with the highest probability that John obtained (by doing some Math-y Bayes' Theorem stuff!).

(c) The next day, John has no more orange candies, so he fills his left pocket with 5 and his right pocket with 2. He then goes to the grocery store to buy some strawberry candies. Knowing that he will put them all in his right pocket, how many must he buy so that on the next roll, he is as close as possible to having as the same chance of drawing one orange candy as he has of drawing strawberry candy?