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A coin is flipped four times. Game 1 pays $20 if at least one head appears and Game 2 pays $500 only if all four are heads. Which do you choose, and why?

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Coin A lands heads with probability 2/3 and coin B with probability 1/3. One is chosen at random and flipped three times, all heads. What is the probability it is coin A?I flip three coins and tell you at least one is heads. What is the probability all three are heads?It costs $1 to play: flip a fair coin four times and win $10 if all four are heads. Should you play?

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