Stat Analysis

The Super Bowl, the annual championship game of the National Football League, begins with a coin toss to determine which team controls the ball. Of the 53 games played between 1967 and 2019, the coin flip was tails 28 times and heads 25 times, close enough to assume the coin toss is fair. The opposing teams in the Super Bowl always come from two "conferences:" the AFC and the NFC. Between 1998 and 2011, the NFC team won the coin toss 14 consecutive times. The streak ended in 2012 when the New England Patriots won the coin toss (though they lost the game).
(a) Given that the Super Bowl is played once per year, on average how many years should we expect to wait before we see another streak of 14 consecutive coin toss wins by one conference? Hint: you probably want to solve this by induction; consider 2, 3, or 4 consecutive wins, generalize to n consecutive wins, and substitute n = 14.
(b) How likely is it that this kind of streak happened by chance? Express your answer in terms of Gaussian o.

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