Consider three football teams A, B and C. In a regular game, A beats B with probability p and beatsC with probability q. C is a better team than B, so p > q. To win the tournament, A needs to wintwo games in a row out of three games against B and C, and it can’t play two games in a row againstthe same team. A can either select to play these three games as B − C − B or C − B − C. Showthat A maximizes the probability of winning the tournament by playing against the better team C,twice.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Consider three football teams A, B and C. In a regular game, A beats B with
C with probability q. C is a better team than B, so p > q. To win the tournament, A needs to win
two games in a row out of three games against B and C, and it can’t play two games in a row against
the same team. A can either select to play these three games as B − C − B or C − B − C. Show
that A maximizes the probability of winning the tournament by playing against the better team C,
twice.
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