The Department of Foreign Languages of a liberal arts college conducted a survey of its recent graduates to determine the foreign language courses they had taken while undergraduates at the college. Of the 520 graduates 210 had at least one year of Spanish. 170 had at least one year of French. 146 had at least one year of German. 43 had at least one year of Spanish and French. 28 had at least one year of Spanish and German. 22 had at least one year of French and German. 5 had at least one year of all three languages. (a) How many of the graduates had at least 1 yr of at least one of the three languages?  graduates (b) How many of the graduates had at least 1 yr of exactly one of the three languages?  graduates (c) How many of the graduates had less than 1 yr of any of the three languages?  graduates

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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.