Assume that we have three coins: The first coin is fair. The second coin is unfair with probability of heads equal to 0.8. The third coin is also unfair with probability of heads equal to 0.3. Consider an experiment involving two successive coin tosses. The result of the first stage of the experiment is determined by the toss of the fair coin. The result of the second stage of the experiment is determined by the toss of a coin, but suppose that the coin that is used depends upon the result of the toss of the fair coin. Specifically, if the toss of the fair coin results in heads, then the second coin is tossed. Otherwise the third coin is tossed. Let Hi and Ti be the events that ith toss resulted in heads and tails, respectively. Answer the following questions. a) Give a sequential description of the experiment using a tree diagram. b) Calculate the probabilities of the possible outcomes of the experiment. c) Calculate P(H2)
Assume that we have three coins: The first coin is fair. The second coin is unfair with
Let Hi and Ti be the
a) Give a sequential description of the experiment using a tree diagram.
b) Calculate the probabilities of the possible outcomes of the experiment.
c) Calculate P(H2)
d) Are the events H1 and H2 independent? Justify your answer analytically.
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