Exercise 5.18.6: Calculating probabilities of independent events. A biased coin is flipped 10 times. In a single flip of the coin, the probability of heads is 1/3 and the probability of tails is 2/3. The outcomes of the coin flips are mutually independent. What is the probability of each event? (b) The first 5 flips come up heads. The last 5 flips come up tails. (c) The first flip comes up heads. The rest of the flips come up tails.
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Exercise 5.18.6: Calculating probabilities of independent events.
A biased coin is flipped 10 times. In a single flip of the coin, the probability of heads is 1/3 and the probability of tails is 2/3. The outcomes of the coin flips are mutually independent. What is the probability of each event?
(b)
The first 5 flips come up heads. The last 5 flips come up tails.
(c)
The first flip comes up heads. The rest of the flips come up tails.
Exercise 5.19.1: Bayes' Theorem - detecting a biased coin.
(a)
Sally has two coins. The first coin is a fair coin and the second coin is biased. The biased coin comes up heads with probability .75 and tails with probability .25. She selects a coin at random and flips the coin ten times. The results of the coin flips are mutually independent. The result of the 10 flips is: T,T,H,T,H,T,T,T,H,T. What is the probability that she selected the biased coin?
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