please answer a through d for both

Another way to define a fair game is that a player's probability of winning must be equal to the player's share of the pot of money awarded to the winner. All money is put into a pot at the start of the game, and the winner claims the entire amount that is in the pot. (Compare this definition to the following: A game involving chance is said to be fair if the expected amount won or lost is zero.) (a) The player puts $20 into the pot and the host put $20 into the pot. The player rolls a six sided die and wins the pot if the die produces a number greater than 3. Is this a fair game? (b) A player at a casino puts $2 into the pot and names a rank from a standard deck (e.g., seven or ace). The casino puts $50 into the pot. If a randomly selected card matches the choice of the player, the player wins the pot. Is this a fair game? (a) What is the player's probability of winning? (Type an integer or a simplified fraction.)(a) X/4 Given that the random variable X has mean u = 200 and SD . = 12, find the mean and SD of each of the following random variables that are defined from X. (b) 2X - 120 (c) X +4 (d) X- X . . . . . (a) = ,0= (Simplify your answers.)Given that the random variable Y has mean u = 150 and SD o = 40, find the mean and SD of each of the following random variables that are defined from Y. (a) 4Y + 30 (b) 2Y Y - + 0.25 (d) 10 -Y . . . . . (a) = , .= (Simplify your answers.)