(a) let {a1, a2} be a partition of a sample space and let b be any event. state and prove the law of total probability as it applies to the partition {a1, a2} and the event b.
there are two coins in a box; one coin is a fair coin, and the other is a biased coin thatcomes up heads 75 percent of the time. fiona chooses a coin at random and tosses it.
(b) what is the probability that the chosen coin flips heads? (hint: the law of totalprobability.)
(c) given that the chosen coin flips heads, what is the conditional probability that it wasthe biased coin? (hint: bayes’ theorem.)
(d) given that the chosen coin flips tails, what is the conditional probability that it wasthe biased coin?