Let's say you flip a coin repeatedly - it's a fair coin, and let's assume it never lands on its edge. So, 50% of tosses are heads, and 50% tails.
(1) How many tosses, on average, would you need to make before you get a sequence of Heads, Tails, Tails?
In other words, if you tossed: Heads, Tails, Heads, Tails, Heads, Tails, Tails - you would score this as 7; and Heads, Tails, Tails as 3
(2) How many tosses, on average, would you need to make before you get a sequence of Tails, Heads, Heads?
(3) How many tosses, on average, would you need to make before you get a sequence of Tails, Tails, Tails?
(4) How many tosses, on average, would you need to make before you get a sequence of Heads, Tails, Heads?
(5) A friend challenges you to a 'race'. You each choose a sequence. An independent third party tosses the coin. The winner is the the person whose sequence comes up first. Is there a sequence or sequences that you can choose that would maximize your chances of winning?
(1) How many tosses, on average, would you need to make before you get a sequence of Heads, Tails, Tails?
In other words, if you tossed: Heads, Tails, Heads, Tails, Heads, Tails, Tails - you would score this as 7; and Heads, Tails, Tails as 3
(2) How many tosses, on average, would you need to make before you get a sequence of Tails, Heads, Heads?
(3) How many tosses, on average, would you need to make before you get a sequence of Tails, Tails, Tails?
(4) How many tosses, on average, would you need to make before you get a sequence of Heads, Tails, Heads?
(5) A friend challenges you to a 'race'. You each choose a sequence. An independent third party tosses the coin. The winner is the the person whose sequence comes up first. Is there a sequence or sequences that you can choose that would maximize your chances of winning?
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