Yowsie! is a game is played by rolling 4 six-sided dice at once. On each die there is a side that depicts a star. Below is the probability distribution, where X represents the number of stars that a player might roll upon rolling all 4 dice. X 0 1 2 3 4 P(X) 0.3164 0.4219 0.2110 0.0469 0.0039

a) (6pts) What is the probability that the number of stars rolled will be less than 2?

b) (6pts) If at least 1 star was rolled, what is the probability that there was a total of 4 stars?

c) (6pts) Suppose that a local casino starts to allow players to play this game for money. Players have to pay $5 to roll the 4 dice but get paid $3 for each start that they roll. Let Y represent the money earned by the casino. Make a probability distribution for Y.

d) (5pts) What is average amount of money the casino can expect to earn every time a player pays $5 to roll the dice?