In Parade Magazine's (Nov. 26, 2000) column "Ask Marilyn," the following question was posed: "I have just tossed a [balanced] coin 10 times, and I ask you to guess which of the following three sequences was the result. One (and only one) of the sequences is genuine."
(1) H H H H H H H H H H
(2) H H T T H T T H H H
(3) T T T T T T T T T T
a. Demonstrate that prior to actually tossing the coins, the three sequences are equally likely to occur.
b. Find the probability that the 10 coin tosses result in all heads or all tails.
c. Find the probability that the 10 coin tosses result in a mix of heads and tails.
d. Marilyn's answer to the question posed was "Though the chances of the three specific sequences occurring randomly are equal... it's reasonable for us to choose sequence (2) as the most likely genuine result." If you know that only one of the three sequences actually occurred, explain why Marilyn's answer is correct.