7. Suppose a jar has 100 coins, of which some are real, with heads and tails sides, but some are fake, with heads on both sides. (a) twice, getting heads both times. What is the probability it's the fake coin? Assume 99 of the coins are real. We choose a coin at random and flip it (b) pick a coin at random, flip it twice, and get heads both times, how many of the 100 coins must be fake for the probability that the coin we picked is fake to be at least 50%? Now suppose we don't know how many of the coins are real and fake. If we

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7. Suppose a jar has 100 coins, of which some are real, with heads and tails sides, but some are
fake, with heads on both sides.
(a)
twice, getting heads both times. What is the probability it's the fake coin?
Assume 99 of the coins are real. We choose a coin at random and flip it
(b)
pick a coin at random, flip it twice, and get heads both times, how many of the 100 coins
must be fake for the probability that the coin we picked is fake to be at least 50%?
Now suppose we don't know how many of the coins are real and fake. If we
Transcribed Image Text:7. Suppose a jar has 100 coins, of which some are real, with heads and tails sides, but some are fake, with heads on both sides. (a) twice, getting heads both times. What is the probability it's the fake coin? Assume 99 of the coins are real. We choose a coin at random and flip it (b) pick a coin at random, flip it twice, and get heads both times, how many of the 100 coins must be fake for the probability that the coin we picked is fake to be at least 50%? Now suppose we don't know how many of the coins are real and fake. If we
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