In some states, such as lowa and Nevada, the presidential primaries are decided by caucuses rather than a primary election. The caucuses determine winners at the precinct level, and turnout is often
low. As a result, it is not uncommon in a close race to have some caucuses end in a tie. The article "A Nevada Tie to Be Decided by Cards"t reported that in Nevada a tie is decided by having each side
draw a card, with the high card winning. In lowa, a tie is decided by a coin toss. In 2016, in the primary race between Hillary Clinton and Bernie Sanders, some Democratic caucuses were in fact decided
by coin tosses.
(a) Suppose two caucuses resulted in a tie between Bernie Sanders and Hillary Clinton. What is the probability that both would be decided in favor of Hillary Clinton?
(b) Suppose two caucuses resulted in a tie between Bernie Sanders and Hillary Clinton. What is the probability that both would be decided in favor of Bernie Sanders?
(c) Suppose two caucuses resulted in a tie between Bernie Sanders and Hillary Clinton. What is the probability that both would be decided in favor of the same candidate?
(d) Suppose that three caucuses resulted in a tie between Bernie Sanders and Hillary Clinton. What is the probability that all three caucuses would be decided in favor of the same candidate?
