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111Three Cards, Three Different SuitsThree cards are drawn without replacement from a standard 52-card deck. What is the probability that all three cards are from different suits?概率简单数值题未尝试免费112Drawing a Pair of AcesTwo cards are drawn without replacement from a standard 52-card deck. What is the probability that both cards are aces?概率简单数值题未尝试免费113Probability of a Poker StraightA 5-card hand is dealt from a standard 52-card deck. What is the probability that the hand is a straight but not a straight flush (i.e., five cards of consecutive ranks, not all of the same suit)? Aces can be high or low (A-2-3-4-5 through 10-J-Q-K-A).概率中等数值题未尝试免费114Expected Cards to See All Four SuitsA standard 52-card deck is shuffled uniformly at random and cards are turned over one at a time from the top. Let X be the number of cards turned over until all four suits have appeared at least once. Find E[X].概率困难derivation未尝试面试订阅115Void in a Bridge HandA 13-card bridge hand is dealt from a standard 52-card deck. What is the probability that the hand contains a void — that is, at least one suit is completely absent from the hand?概率困难derivation未尝试面试订阅116Both Top Cards RedA standard 52-card deck is shuffled uniformly at random. What is the probability that the top two cards are both red?概率简单数值题未尝试免费117Face Card Then AceTwo cards are drawn sequentially without replacement from a standard 52-card deck. What is the probability that the first card is a face card (J, Q, or K) and the second card is an ace?概率简单数值题未尝试免费118Exactly Two Suits in a Poker HandA 5-card hand is dealt from a standard 52-card deck. What is the probability that exactly two suits are represented in the hand?概率中等数值题未尝试免费119Four Cards, All Different RanksFour cards are drawn without replacement from a standard 52-card deck. What is the probability that all four cards have different ranks?概率中等数值题未尝试免费120Expected Distinct Ranks in a Seven-Card HandSeven cards are drawn without replacement from a standard 52-card deck. Let R be the number of distinct ranks represented among the seven cards. Find E[R].概率困难derivation未尝试面试订阅121No Face Cards in Three-Card HandThree cards are drawn without replacement from a standard 52-card deck. What is the probability that none of the three cards is a face card (jack, queen, or king)?概率简单数值题未尝试免费122Exactly One Ace in a Poker HandA 5-card poker hand is dealt from a standard 52-card deck. What is the probability that the hand contains exactly one ace?概率中等数值题未尝试免费123Three-of-a-Kind in PokerA 5-card poker hand is dealt from a standard 52-card deck. What is the probability of getting exactly three-of-a-kind (three cards of one rank and two cards of two other distinct ranks, excluding a full house)?概率中等数值题未尝试免费124Two-Pair in PokerA 5-card poker hand is dealt from a standard 52-card deck. What is the probability of getting two-pair (exactly two different pairs plus one card of a third rank)?概率困难数值题未尝试面试订阅125All Four Suits in a Seven-Card HandSeven cards are drawn without replacement from a standard 52-card deck. What is the probability that all four suits are represented among the seven cards?概率困难derivation未尝试面试订阅126Sum of Seven on Two DiceYou roll two fair six-sided dice. What is the probability that the sum of the two dice equals 7?概率简单数值题未尝试免费127Three Heads in Five FlipsYou flip 5 fair coins simultaneously. What is the probability of getting exactly 3 heads?概率简单数值题未尝试免费128Maximum of Three Dice Equals FourYou roll three fair six-sided dice. What is the probability that the maximum of the three values equals exactly 4?概率中等数值题未尝试免费129Doubles Given an Even SumYou roll two fair six-sided dice and are told that their sum is even. What is the probability that both dice show the same number?概率中等数值题未尝试免费131At Least One Head in Three FlipsYou flip 3 fair coins. What is the probability that at least one coin lands heads?概率简单数值题未尝试免费