Question 5 (10 marks). Prior to tossing a coin, it is believed that the chance of tossing a head

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Question 5 (10 marks). Prior to tossing a coin, it is believed that the chance of tossing a head is equally likely to be $\frac{1}{3}$ or $\frac{2}{3}$. The coin is tossed twice, and both tosses result in a head. Determine the posterior probability of tossing a head.