1. In a TV game show, 67 of the contestants are males and 33 are females. Only those who get the correct answer in a round will proceed to the next round. In the first round, 40 males and 29 females were eliminated. Momo and her 4 male and 2 female friends or dabarkads made it to the next round. If at this point, a special prize (i.e., one year supply of hair products) will be given to one of the qualified contestants at random. What is the probability that Momo or a female contestant, or one of Momo dabarkads will bag the special prize? a). A class in Math 10 is composed of 20 freshmen, 20 juniors, and 10 seniors. The final grades show that 5 of the freshmen, 4 of the juniors, and 6 of the seniors receive a grade of 1.00 for the course. If a student is chosen at random from this class and is found to earn a grade of 1.00, what is the probability that he or she is a senior? b) Jovy is currently enrolled in four Math subjects. To maintain a good standing in the Mathematics program, he has to pass at least three of his Math subjects. Suppose that the probability of passing all his Math subjects equal to the probability of passing three Math subjects. Assume further that the probability of Jovy passing three subjects is 1/2 of the probability of passing two subjects. The probability of passing two subjects is 1/3 of the probability of passing one subject. The probability of passing one subject is 3/4 of the probability of failing all his subjects. Construct the discrete probability distribution of the random variable that counts the number of Math subjects that Jovy will pass. Is Jovy expected to have a good standing in the Mathematics program? Explain