Two dice are rolled until either a total of 12 or two consecutive totals of 7. What is the probability the 12 is rolled first?
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Every generaion of red amoeba has a 5% chance of spawning 5 more red amoeba, a 10% chance of spawning 3 blue amoeba, a 1% chance of doing both, and a 84% chance of not spawning.
Every generaion of blue amoeba has a 3% chance of spawning 5 more blue amoeba, a 2% chance of spawning 10 red amoeba, a 1% chance of doing both, and a 94% chance of not spawning.
Your petri dish starts with one red amoeba. What is the expected number of red and blue amoeba observed before all amoeba die off? (answer), (solution)
The game of one-card poker has a three-card deck, an ace, deuce, and trey. The ace is lowest and the trey is highest. Each of two players ante $1 into the pot. Then, each player gets one card. The order of betting is predetermined, with player 1 to act first. Player 1 may either bet $1 or check. If player 1 bets, player 2 may either call or fold. If player 1 checks, player 2 may either bet $1 or check. If player 1 checks, and player 2 bets, then player 1 may either call or fold. If both players check, or one bets and one calls, then the higher card wins the pot. Assuming both players are perfect logicians, what is the optimal strategy for each player?
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On May 23, 2009, a craps player held the dice for 154 rolls at the Borgata casino in Atlantic City (source). What is the probability of going 154 rolls or longer in craps? Please give an expression of the answer and/or a numeric answer.
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Imagine a keno game where the numbers are drawn WITH replacement. In other words, 20 balls are drawn from an urn with balls numbered 1 to 80, one at time. As each ball is drawn the number is noted, and then the ball is returned to the urn. The player picks four different numbers from 1 to 80. For each number picked it is considered a match if the casino draws that number at least once. What is the probability for each possible outcome of 0 to 4 matches?
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