Question

We find ourselves at a fancy casino in Las Vegas, and decide to try our luck at a card game played with a standard deck of cards. The card game has a number of options to choose from, and we intend to play the game with the best odds. However, we are going to need to calculate the odds before we play. As a reminder, a "standard" deck of playing cards consists of 52 Cards in each of the 4 suits called Spades, Hearts, Diamonds, and Clubs. Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King.

The games all involve the same concept - We are asked to randomly choose 10 cards from the standard deck of cards. After each card has been chosen, that card is replaced and the deck is shuffled before we choose the next card. The games that we can choose from are as follows:

1. You must choose exactly 1 Ace.
2. You must choose more than 3 Hearts.
3. You must choose no Kings.
4. You must choose less than 4 Red Cards.
5. You must choose at least 5 Black Cards.

Calculate the probability of success for each of the 5 games (3 points each), and indicate which game you wish to play