5.56 Rosencrantz and Guildenstern In the opening scene of Tom Stoppard’s play Rosencrantz and Guildenstern Are Dead, about two Elizabethan contemporaries of Hamlet, Guildenstern flips a coin 91 times and gets a head each time. Suppose the coin was balanced.

a. Specify the sample space for 91 coin flips, such that each outcome in the sample space is equally likely.

How many outcomes are in the sample space?

b. Show Guildenstern’s outcome for this sample space.

Show the outcome in which only the second flip is a tail.

c. What’s the probability of the event of getting a head 91 times in a row?

d. What’s the probability of at least one tail in the 91 flips?

e. State the probability model on which your solutions in parts c and d are based.