1.A well-shuffled ordinary deck of 52 cards is divided randomly into four piles of 13 each.
Counting jack, queen, and king as 11, 12, and 13, respectively, we say that a match occurs in a pile if the jth card is j.
What is the expected value of the total number of matches in all four piles?
2.Condsider a slot machine in a casino which is contructed with a lever and four rotating wheels.
On each wheel, pictures of an apple, a banana, a cherry, an orange, a pear and a grape are drawn.
By pulling the lever, a player can cause the wheels to turn.
The player can see the outcomes of each turning through the display revealing the pictures on the respective wheels.
To win a game, the player must get at least two cherries.
Assume that each wheel rotates independently and that the probability of an occurence of any fruit is identical.
What is the probability of winning the game?