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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130Expected Distinct Faces on Four DiceYou roll four fair six-sided dice. What is the expected number of distinct face values that appear among the four dice?概率困难数值题未尝试免费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132Large Sum Given Odd ProductYou roll two fair six-sided dice and are told that their product is odd. What is the probability that their sum exceeds 8?概率中等数值题未尝试免费133Exactly One Pair Among Four DiceYou roll 4 fair six-sided dice. What is the probability that exactly two of the four dice show the same value and the other two dice each show values different from each other and from the pair?概率中等数值题未尝试免费134Near-Even Split in Seven Coin FlipsYou flip 7 fair coins. What is the probability that the number of heads and the number of tails differ by at most 1?概率中等数值题未尝试免费135Conditional Third Roll Reaching TenYou roll two fair six-sided dice. If their sum is even, you roll a third die and your score is the sum of all three dice. If their sum is odd, your score is just the sum of the first two dice. What is the probability that your score is at least 10?概率困难数值题未尝试免费136Two-Dice Sum Is a Perfect SquareYou roll two fair six-sided dice. What is the probability that their sum is a perfect square?概率简单数值题未尝试免费137Exactly Two Heads in Four FlipsYou flip 4 fair coins. What is the probability that exactly 2 of them land heads?概率简单数值题未尝试免费138Exactly One Pair Among Three DiceYou roll 3 fair six-sided dice. What is the probability that exactly two of the three dice show the same value while the third die shows a different value?概率中等数值题未尝试免费