The game of BINGO involves drawing numbered and lettered buttons at random from a barrel. The B numbers are 1-15, the I numbers are 16-30, the N numbers are 31-45, the G numbers are 46-60, and the O numbers are 61-75. Buttons are not replaced after they have been selected. What is the probability of each of the following events on the initial selections?

a. Drawing a B button

b. Drawing two B buttons in a row

c. Drawing a B or an O

d. Drawing a B, then a G, then an N, in that order

e. Drawing anything but a B on each of the first five draws At Least Once Problems. A common problem asks for the probability that an event occurs at least once in a given number of trials. Suppose the probability of a particular event is p (for example, the probability of drawing a heart from a deck of cards is 0.25). Then the probability that the event occurs at least once in N trials is 1 - (1 – pf For example, the probability of drawing at least one heart in 10 draws (with replacement) is 1 - (1 - 0.25)10 = 0.944

Use this role to solve Exercises 31 and 32.