A gambling game is played in which there is a group of 100 cards with one $25 winning card, two $10 winning cards, and three $5 winning cards. After paying a certain fee, a player selects one card at random. If it is one of the winning cards, the player receives the designated amount. If it is one of the other cards, the player wins nothing. The card is returned to the deck, the cards shuffled, and they are ready for the next play.
a. Find the probability distribution for y, the number of dollars won (use the rule for equally likely events).
b. If a large number of plays are purchased, what are the expected winnings per play, or in statistical terms, what is the expected value of y?
c. Would it be reasonable to pay $1 to play this game?
d. Find the variance of this probability distribution.
e. What proportion of the time will the winnings be within two standard deviations of the expected value?