Suppose that you have purchased a 40-piece box of salt water taffy; taffy is a typeof soft, chewy candy that became popular in the United States in the 1800s. The box is advertised as containing a random assortment of 8 flavors. Calculate the probability that at least one flavor is missing from the box.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.

Which choice names the hypotenuse of triangle xyz? a. segment yx b. segment yz c. segment ab d. segment zx

How many zeroes do we write when we write all the integers 1 to 243 in base 3?