- Mysterioso the Magician is walking down the street with a box containing 25 identical looking coins: 24 are fair coins (which flip heads with probability 0.5 and tails with probability 0.5) and one is a trick coin which always flips heads. Renata the Fox skillfully robs Mysterioso of one of the coins in his box (chosen uniformly at random). She decides she will flip the coin k times to test if it is the trick coin.
(a) What is the probability that the coin Renata has is the trick coin, given that it flips heads all k times? (b) What is the smallest number of times she needs to flip the coin to believe there is at least a 90% chance she has the trick coin, given that it flips heads on each of the flips?
