Exercise 3. If we changed the setup slightly, to have a 60% chance of getting the fair coin rather than a 40% chance, how would this probability P(G|E3) change? That is, how does this work out if the bag of coins has 60% fair coins? What if we change it to have 90% fair coins (and the remainder biased with probability 3/4 of heads)? Later we'll see how this setup can be used for hypothesis testing. The hypotheses here are "the coin is fair" and "the coin is biased with probability 3/4 of heads". The probability of getting a fair or biased coin will be called the prior probabilities of the hypotheses. This exercise shows the influence of the prior probabilities on the posterior probability of the hypothesis, that is, the conditional probability of the hypothesis given the result of the experiment. Exercise 3. If we changed the setup slightly, to have a 60% chance of getting the fair coin rather than a 40% chance, how would this probability P(G|E3) change? That is, how does this work out if the bag of coins has 60% fair coins? What if we change it to have 90% fair coins (and the remainder biased with probability 3/4 of heads)? Later we'll see how this setup can be used for hypothesis testing. The hypotheses here are "the coin is fair" and "the coin is biased with probability 3/4 of heads". The probability of getting a fair or biased coin will be called the prior probabilities of the hypotheses. This exercise shows the influence of the prior probabilities on the posterior probability of the hypothesis, that is, the conditional probability of the hypothesis given the result of the experiment