This is in Statistics and Probability. Answer the problems below. This is only multiple choice. Provide necessary solution for each items. Thank you and Godbless. Follow the numbering.

21. A class in advanced mathematics is composed of 8 juniors, 20 seniors, and 12 graduate students. The final grades show that 3 of the juniors, 7 of the seniors and 6 of the graduate students received an A for the course. If a student is chosen at random from this class and is found to have earned an A, what is the probability that he or she is a senior? A) 9/16 C) 7/16 B) 5/8 D) 3/16 22. A class in advanced mathematics is composed of & juniors, 20 seniors, and 12 graduate students. The final grades show that 3 of the juniors, 7 of the seniors and 6 of the graduate students received an A for the course. If a student is chosen at random from this class and is found to have earned an A, what is the probability that he or she is a graduate student? A) 11/16 C) 3/16 B) 3/8 D) 5/8 23. If an aircraft is present in a certain area, a radar correctly detects its presence with probability 0.99. If it is not present, the radar falsely detects an aircraft presence with probability 0.08. We assume that an aircraft is present with probability 0.05. What is the probability of false alarm (i.e., the radar detects an aircraft but it is not present, or simply a false indication of aircraft presence). Assign the following events: A = { an aircraft is present } B = { the radar detects an aircraft } A) 0.010 C) 0.050 B) 0.076 D) 0.004 24. If an aircraft is present in a certain area, a radar correctly detects its presence with probability 0.99. If it is not present, the radar falsely detects an aircraft presence with probability 0.08. We assume that an aircraft is present with probability 0.05. What is the probability of missed detection (nothing is detected, even though an aircraft is present)? Assign the following events: A = { an aircraft is present } B = { the radar detects an aircraft } A) 0.5 C) 0.05 0.0005 D) 0.005