Kaylee read a report that said the probability that a randomly selected American is left-handed is 14\%14%14, percent. She was curious how many left-handed students to expect in a class of 252525 students. She simulated 404040 classes of 252525 students where each student selected had a 0.140.140, point, 14 probability of being left-handed. Kaylee counted how many left-handed students were in each simulated class. Here are her results: Use her results to estimate the probability that there are fewer than 333 left-handed students in a class of 252525 students. Give your answer as either a fraction or a decimal. P(\text{fewer than } 3 \text{ left-handed})\approxP(fewer than 3 left-handed)≈P, left parenthesis, start text, f, e, w, e, r, space, t, h, a, n, space, end text, 3, start text, space, l, e, f, t, negative, h, a, n, d, e, d, end text, right parenthesis, approximately equals

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.