In a class, there are twelve freshmen boys, sixteen freshmen girls, and nine sophomore boys. How many sophomore girls must be present if gender and class are to be independent when a student is selected at random?

This exercise refers to a standard deck of playing cards. Assume that 8 cards are randomly chosen from the deck.How many hands contain exactly two 2s and two 5s?

In a survey of 252 professional athletes, it was found that 119 of them owned a convertible, 122 of them owned a giant screen TV, and 115 owned a sporting goods store. 21 owned a convertible and a store, 44 owned a TV and a store, and 73 owned a covertible and a TV. 13 owned all three items. How many athletes did not own any of the three items? How many owned a covertible and a TV, but not a store? How many athletes owned a convertible or a TV? How many athletes owned exactly one type of item in the survey? How many athletes owned at least one type of item in the survey? How many owned a TV or a store, but not a convertible?

Bowl A contains 2 red chips; bowl B contains two white chips; and bowl C contains 1 red chip and 1 white chip. A bowl is selected at random, and one chip is taken at random from that bowl.