Problem 1 [35 pts (5 pts each)]: Weekend trip to Vegas. i. An American roulette wheel has 38 numbered slots: 2 are green, 18 are red, and 18 are black. When the wheel is spun, a marble, rolling in the opposite direction, will eventually land in one of the slots. We record the sequence of outcomes when the wheel is spun five times. How many 5-spin sequence outcomes are possible? ii. How many 5-spin outcomes are all of the same color? iii. How many times must the wheel be spun before we can be sure that the marble landed on one of the numbered slots at least five times? Explain your answer. iv. A standard 52-card deck has four suits (Hearts, Diamonds, Clubs, and Spades) and each suit has 13 ranks (2,3,4,5,6,7,8,9,10,Jack, Queen,King, Ace). The face cards are Jack, Queen, and King. How many ways are there to be dealt any 2 cards from a 52-card deck? (We are counting as distinct the same two cards received in a different order.) v. How many ways are there to be dealt Blackjack? To be dealt Blackjack, either the first card is an Ace and the second card is a face card or a 10, or the first card is a face card or a 10 and the second card is an Ace. (Again we are counting as distinct the same two cards received in a different order.) vi. How many ways can you be dealt two cards such that the first card is a spade and the second card is a face card? vii. How many ways can you pick three cards such that the first card is a spade, the second card is a one-eyed Jack, and the third card is a face card? (There are two one-eyed Jacks in a standard deck: the Jack of Hearts and the Jack of Spades. Hint: Break the problem down into 3 disjoint cases for the type of card received 1st, 2nd, and 3rd. Problem 1 [35 pts (5 pts each)]: Weekend trip to Vegas. i. An American roulette wheel has 38 numbered slots: 2 are green, 18 are red, and 18 are black. When the wheel is spun, a marble, rolling in the opposite direction, will eventually land in one of the slots. We record the sequence of outcomes when the wheel is spun five times. How many 5-spin sequence outcomes are possible? ii. How many 5-spin outcomes are all of the same color? iii. How many times must the wheel be spun before we can be sure that the marble landed on one of the numbered slots at least five times? Explain your answer. iv. A standard 52-card deck has four suits (Hearts, Diamonds, Clubs, and Spades) and each suit has 13 ranks (2,3,4,5,6,7,8,9,10,Jack, Queen,King, Ace). The face cards are Jack, Queen, and King. How many ways are there to be dealt any 2 cards from a 52-card deck? (We are counting as distinct the same two cards received in a different order.) v. How many ways are there to be dealt Blackjack? To be dealt Blackjack, either the first card is an Ace and the second card is a face card or a 10, or the first card is a face card or a 10 and the second card is an Ace. (Again we are counting as distinct the same two cards received in a different order.) vi. How many ways can you be dealt two cards such that the first card is a spade and the second card is a face card? vii. How many ways can you pick three cards such that the first card is a spade, the second card is a one-eyed Jack, and the third card is a face card? (There are two one-eyed Jacks in a standard deck: the Jack of Hearts and the Jack of Spades. Hint: Break the problem down into 3 disjoint cases for the type of card received 1st, 2nd, and 3rd
