Many studies investigating extrasensory perception (ESP) have been conducted. A typical ESP study is carried out by subjecting an individual claiming to have ESP to a series of trials and recording the number of correct identifications made by the subject. Furthermore, when a subject is strictly guessing on each trial, the number of correct identifications can be modeled with a binomial probability model with the probability of a correct identification being ???? = 0.5 on each trial. If a subject is guessing on each of 20 trials in an ESP study, determine

(a) the probability of 20 correct identifications.

(b) the probability of 18 correct identifications.

(c) the probability of at least 18 correct identifications.

(d) the mean number of correct identifications.