The probability of an economic decline in a certain year is 0.21. There is a probability of 0.61 that we will elect a republican president in the same year. If we elect a republican president, there is a 0.34 probability of an economic decline. Let D represent the event of an economic decline and R represent the event of election of a Republican president. (a) Are R and D independent events? O Yes, because P(D) * P(D|R). O Yes, because P(D) = P(D|IR). O No, because P(D) + P(DIR). O No, because P(D) = P(D|R). (b) What is the probability of a Republican president and economic decline in the year? (c) If we experience an economic decline in the year, what is the probability that there will a Republican president? (Round your answer to four decimal places.) (d) What is the probability of economic decline or a Republican president in the year? Hint: You want to find P(D U R).

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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.