1. (a) Consider a play-off tournament (where the loser is out, and the winner advances to the next round) with n rounds and 2" players. Two players are chosen at random. Calculate the probability that they play against each other: (i) in the first round; (ii) in the final, i.e. the last round; (iii) in any round.

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A: To find the coefficient of x10 in the expansion of 2x+1x100 we will use(r+1)th term in the expansion…

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A: The given integral is: I=∫x3x2-9dx

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A: Solution: The objective is to find the value of the given expression

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A: We find the value of r in above questions.

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A: Given that: 57-24

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Q: Find A.

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A: Please see the answer below.

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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.