Runs. In a row of six plants two are infected with a leaf disease and four are healthy. If we restrict attention to the portion of the sample space for exactly two infected plants, the model of randomness (or lack of contagion) assumes that any two positions, for the infected plants in the row are as likely as any other.

(a) Using the symbols I for infected and H for healthy, list all possible occurrences of two I’s and four H’s in a row of 6.

(b) A random variable of interest is the number of runs X that is defined as the number of unbroken sequences of letters of the same kind. For example, the arrangement IHHHIH has four runs, IIHHHH has two. Find the value of X associated with each outcome you listed in part (a).

(c) Obtain the probability distribution of X under the model of randomness.