Question

(b) at most a total of 4. 4. The class registrations of 100 students are analyzed. It is found that 50 students study Applied Mechanics, 45 study Chemistry, and 15 studied both Applied Mechanics and Chemistry (a) If one of these students is selected at random, find the probability that i. the student took applied mechanics or chemistry. ii. the student did not take either of these subjects. iii. the student took chemistry but not applied mechanics. (b) Are studying Applied Mechanics and studying Chemistry mutually exclusive events? Why or why not? Hint: You may want to draw a Venn diagram. 5. The probability that Intel will locate in Shanghai, China, is 0.4, the probability that it will locate in Beijing, China, is 0.5, and the probability that it will locate in either Shanghai or Beijing or both is 0.7. Answer the following. (a) Let S Shanghai and B-Beijing. From the statement above, list ALL of the probabilities that are given. Example: What is P(B)? (b) What is the probability that Intel will locate in both cities? (c) What is the probability that Intel will locate in neither city?

4&5

Answer 1

As per HOMEWORKLIB POLICY, if a post contains more than 1 distinct questions, we have to solve the first one

Solving Question 4

4) Let A : event that a randomly selected student studies Applied Mechanics B : event that a randomly selected student studies Chemistry 50 students study Applied Mechanics P(A)-50/100-0.5 45 students study Chemistry P(B) 45/100 0.45 15 students study Applied Mechanics and Chemistry P(AnB) 15/100 0.15 To find P(randomly selected student took applied mechanics or chemistry) - P(A OR B) -P(A) + P(B)-P(An B) a)i) 0.50.45 0.15 P(randomly selected student took applied mechanics or chemistry) 0.8 ii) To find P(randomly selected student neither took applied mechanics nor chemistry) 1- P(randomly selected student took applied mechanics or chemistry) -1 0.8 P(randomly selected student neither took applied mechanics nor chemistry) 0.2 ii) 45 students took Chemistry 15 students Applied Mechanics and Chemistry Thus (45-15 30) students took only Chemistry P(randomly selected student took chenistry but not applied mechanics) -30/100 P(randomly selected student took chenistry but not applied mechanics) 0.3 b) For mutually exclusive events, the probability of these two events happening together is 0 In the given example, a student can take Applied Mechanics and Chemistry both at the same time there are 15 students who have taken both subjects Thus P(AnB) 15/100 0.15 Thus A and B are not Mutually Exclusive events Studying Applied Mechanics and studying Chemistry are NOT Mutually Exclusive events