1. Imagine that a family of three (Alice, Bill, and Chester) plays bingo at home every night. Each night, the chance that

any one of the three players will win is

1/

.

a. Using A for Alice wins, B for Bill wins, and C for Chester wins, develop a tree diagram that shows the nine

possible outcomes for two consecutive nights of play.

b. Is the probability that “Bill wins both nights” the same as the probability that “Alice wins the first night and

Chester wins the second night”? Explain.

If the ratio of sum of the first m and n terms of an ap is m2 : n2 , show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1).

Mariah is randomly choosing three books to read from the following: 5 mysteries, 7 biographies, and 8 science fiction novels. which of these statements are true? check all that apply. there are 20c3 possible ways to choose three books to read. there are 5c3 possible ways to choose three mysteries to read. there are 15c3 possible ways to choose three books that are not all mysteries. the probability that mariah will choose 3 mysteries can be expressed as . the probability that mariah will not choose all mysteries can be expressed as 1 −

Three students, javier, sam, and corrine, participated in a fundraiser where people donated a certain amount of money per lap that the student ran. each student also had some initial donations that were collected before the run. the equations that represent each student's total donation, y, based on the number of laps ran, x, is shown below. match each equation with the correct rate of change for that student.