Directions: Construct the probability distribution for the random variables described in each of the following situations. Draw the corresponding histogram for each probability distribution.

1. Suppose three cell phones are tested at random where D represent the defective cell phone and N represent the non-defective cell phone. Let X represents the number of defective cell phones that occur., show the values of the random variable X.

2. Two balls are drawn in succession without replacement from an urn containing 5 red balls and 6 blue balls. Let Z be the random variable representing the number of blue balls. Find the values of the random variable Z.

Directions: Determine the sample space illustrated in each situation below.

a. Among the applicants of an immersion, there are only two vacant positions. Three males and two female applicants qualify for the final interview. Because of scheduling problems, only two applicants can be interviewed immediately. The personnel manager selects these two by assigning a numbered ticket to each applicant, and then randomly drawing two tickets.

b. An experiment consists of asking 2 parents if they are in favor of two more years in the K-12 curriculum. Using "N" for no, "Y" for yes and "U" for undecided.

c. A farmer has three fields, each of which must be planted with rice or corn. He does not plant the same crop in all three fields. Generating a tree diagram, list all the elements of the sample space S.