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Question: 888can anybody help me to solve these seven questionsyour helpful...

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888-Can anybody help me to solve these seven questions,your helpful answers will be greatly appreciated!!!

here are the probelms:
7. Three numbers are randomly selected once from 0 to 9. Find the probabilities of the following two events Ai three numbers dont contain 0 and 5; A2 three numbers dont contain 0 or 5 8. 6 students live a dorm, find the probabilities of the following events: (1) The birthday of at least one student is in October; (2) Among 6 students, the birthdays of 4 students are exactly in October; (3) Among 6 students, the birthdays of 4 students are exactly in a same month. 9. A batch of products contain products A, B, and C. Suppose that products A, B, and C account for 60 %,30%, and 10 of total products, respectively. Now, a product that randomly withdrawn is not product C, find the probability that this product is product A. 10. A dorm is equipped with two warning systems. The working probabilities of systems 1 and 2 are 0.92 and 0.93, respectively. Under the condition that system 1 is down, the probability that system 2 is working is 0.85. Find the probability that (1) systems 1 and 2 are working: (2) system 2 is down and system 1 is working: (3) system 1 is working given that system 2 is down. 11. Let 0 <.POA) <1. Show that events A and Bare independent if and only ifwe have POBI AD PCBA) probabilities POA) and POB) 13. Let POA) 0 and POB) 0. Show that (1) if events A and B are in then A and B are not mutually exclusive dependent, (2) if events A and B are mutually exclusive, then A and B are A and B are dependent
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