大專statistics probability問題

A man plays a game in the following manner: he pays 3 dollars to roll two fair
dice of different colours and he wins n2 dollars only if the same number n
shows up on both dice. Let Y , in dollars, be the random variable which denotes
the net gain of the game when the man plays it once.


(i) Construct a probability distribution for Y .

(ii) Hence calculate the expected net gain of the game.

(iii) Suppose that 25 men play the above game independently.

(1) Find the probability that the net gains of at least two of them are greater
than 5 dollars. Correct your answer to 4 decimal places. (Hint: What is
the probability that the net gain of a man is greater than 5 dollars?)

(2) Find the mean and standard deviation of the number of persons (out of
25) whose net gains are greater than 5 dollars.