Question 126
8 coins are placed on a line from left to right.
In the sequel, we keep on repeating the following action:
Choose at random a coin showing a head and satisfying the following condition:
Condition: Either there is no coin on its right showing a tail, or there is no coin on its left showing a tail.
Suppose we keep on repeating this action until there remains no coin showing a head and satisfying the condition stated above. Determine the expectation of the number of coins showing a head when the actions end.
In the sequel, we keep on repeating the following action:
Choose at random a coin showing a head and satisfying the following condition:
Condition: Either there is no coin on its right showing a tail, or there is no coin on its left showing a tail.
Suppose we keep on repeating this action until there remains no coin showing a head and satisfying the condition stated above. Determine the expectation of the number of coins showing a head when the actions end.