The defective rate in a manufacturing process of computer chips is 5%. These chips are fixed on a board, each board containing 25 chips. A board will function if at most two chips are defective, but will not function if there are more than two defective chips among the 25.

a) Let W be the profit made by the sale of a randomly selected board. If the board is defective then the profit is zero. If the board functions properly, then the profit is $5.00. Calculate the mean of W.

b) Find the probability that two randomly selected boards will both function.