Gavin has a bag that contains orange chews, cherry chews, and peach chews. He performs an experiment. Gavin randomly removes a chew from the bag, records the result, and returns the chew to the bag. Gavin performs the experiment 80 times. The results are shown below: An orange chew was selected 19 times.
A cherry chew was selected 13 times.
A peach chew was selected 48 times.

Based on these results, express the probability that the next chew Gavin removes from the bag will be cherry chew as a decimal to the nearest hundredth.

The resumâ´es of two male applicants for a college teaching position in chemistry are placed in the same file as the resumâ´es of two female applicants. two positions become available, and the first, at the rank of assistant professor, is filled by selecting one of the four applicants at random. the second position, at the rank of instructor, is then filled by selecting at random one of the remaining three applicants. using the notation m2f1, for example, to denote the simple event that the first position is filled by the second male applicant and the second position is then filled by the first female applicant, (a) list the elements of a sample space s; (b) list the elements of s corresponding to event a that the position of assistant professor is filled by a male applicant; (c) list the elements of s corresponding to event b that exactly one of the two positions is filled by a male applicant; (d) list the elements of s corresponding to event c that neither position is filled by a male applicant; (e) list the elements of s corresponding to the event a â© b; (f) list the elements of s corresponding to the event a âş c; (g) construct a venn diagram to illustrate the intersections and unions of the events a, b, and c.