One of the most common laboratory tests performed on any routine medical examination is a blood count. the two main aspects of a blood count are (1) counting the number of white blood cells (the "white count") and (2) differentiating the white blood cells that do exist into five categories—namely, neutrophils, lymphocytes, monocytes, eosinophils, and basophils (called the "differential"). both the white count and the differential are used extensively in making clinical diagnoses. we concentrate here on the differential, particularly on the distribution of the number of neutrophils k out of 100 white blood cells (which is the typical number counted).
a. what distribution the number of neutrophils follows.
b. with 6 cells rather than 100, what is the probability that the third and fifth cells considered will be neutrophils and the remaining cells non-neutrophils, given a probability of 0.6 that any one cell is a neutrophil?
c. what is the probability that any 3 cells out of 6 will be neutrophils?