The following two problems will refer to a standard deck of cards. Each card in such a deck hasa rank and a suit. The 13 ranks, ordered from lowest to highest, are 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace. The 4 suits are clubs (♣), diamonds (♢), hearts (♡), and spades (♠). Cards with clubs or spades are black, while cards with diamonds or hearts are red. The deck has exactly one card for each rank–suit pair: 4 of diamonds, queen of spades, etc., for a total of 13 · 4 = 52 cards 1. Sara and Petros each have a standard deck of cards. Independently, each of them selects a card uniformly at random from their respective decks. What is the probability that the rank of Sara’s card is strictly higher than the rank of Petros’s card? 2. Suppose you select a card uniformly at random from a standard deck, and then without putting it back, you select a second card uniformly at random from the remaining cards. What is the probability that both cards have rank no higher than 10, and at least one of the cards is red?
The following two problems will refer to a standard deck of cards. Each card in such a deck hasa rank and a suit. The 13 ranks, ordered from lowest to highest, are 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace. The 4 suits are clubs (♣), diamonds (♢), hearts (♡), and spades (♠). Cards with clubs or spades are black, while cards with diamonds or hearts are red. The deck has exactly one card for each rank–suit pair: 4 of diamonds, queen of spades, etc., for a total of 13 · 4 = 52 cards
1. Sara and Petros each have a standard deck of cards. Independently, each of them selects a card uniformly at random from their respective decks. What is the
2. Suppose you select a card uniformly at random from a standard deck, and then without putting it back, you select a second card uniformly at random from the remaining cards. What is the probability that both cards have rank no higher than 10, and at least one of the cards is red?
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