2. If A, B, and C are mutually exclusive events with P(A)=0.2, P(B)=0.3, and P(C)=0.4, determine the following probabilities: (a) P(A UB UC) (b) P(ABnC) (c) P[(AUB) nC] (d) P(A'nB'nc')
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- 3.74 An experiment results in one of three mutually exclusive events A, B, and C. It is known that P(A) = .30, P(B) = .55, and P(C) = .15, Find each of the following probabilities: а. Р(AU B) b. P(AN B)) с. Р(A|В) d. P(BUC)) e. Are B and C independent events? Explain.3. If A and B are mutually exclusive events with P(A) = .3 and P(B) = 0.5, then P(A N B) = %3D .30 .15 .20If A, B, and C are mutually exclusive events with P(A) = 0.3, P(B) = 0.2, and P(C) = 0.4, determine the following probabilities:
- If A and B are two mutually exclusive events with P(A)= 0.5 and P(B)=0.4, find the following probabilities: a) P(A \textrm{ and } B) = 0.5 b) P(A \textrm{ or } B) = c) P( \textrm{not }A ) = d) P( \textrm{not }B ) = 0.4 e) P( \textrm{not }(A \textrm{ or } B)) = 0.4 f) P( A \textrm{ and } (\textrm{not }B) ) =The prior probabilities for events A1 and Ag are P(A1) = 0.50 and P(A2) = 0.50. It is also known that P(A n A2) = 0. Suppose P(B|A1) = 0.10 and P(B|A2) = 0.70. a. Are events Aj and Ag mutually exclusive? Yes Explain. (i) P(A1 N A2) = 0 (ii) P(A1) + P(A2) = 1 (iii) P(A2) + P (A2 | A1) (iv) P(A2) + P(A2 | A1) choice (i) b. Compute P(A1 n B) (to 2 decimals). 0.165 Compute P(A2 N B) (to 2 decimals). 0.4819 c. Compute P(B) (to 2 decimals). 0.415 d. Apply Bayes' theorem to compute P(A1|B) (to 4 decimals). Also apply Bayes' theorem to compute P(A2|B) (to 4 decimals).7. PAGASA is planning to place at five rain gauge in different locations within Metro Manila. The rain gauge in different location R1, R2, R3, R4 and Rs will operate 0.45, 0.30, 0.20, 0.25 and 0.30, respectively, at a time. If rain pours in those locations has probabilities of 0.2, 0.1, 0.3, 0.2, and 0.2, respectively, what is the probability that it will operate and measure rain water?
- 6. A large group of people is to be checked for two common symptoms of a certain disease. It is thought that 20% of the people possess symptom A alone, 30% possess symptom B alone, 10% possess both symptoms, and the remainder have neither symptoms. For one person chosen at random from this group, find these probabilities (a) The person has neither symptom. (b) The person has at least one symptom. (c) The person has both symptoms, given that the person has symptom B.1) Given two events A and B: P(A) = .3, p(B) = .5, P(A|B) = .7 Then a) P(A n B) = b) P(B|A)=5. A decision maker subjectively assigned the following probabilities to the all the four possible outcomes of an activity: P(E1) = 0.35, P(E2) = 0.12, P(E3) = 0.44, and P(E4) = 0.20. (a) Are these probability assignments valid? Yes or No. (b) Give reason for your answer in 5(a).
- Students taking the Graduate Management Admissions Test (GMAT) were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows. Answer questions 6-9. Undergraduate Major Business Engineering Other Totals Full-Time 352 197 251 800 Intended Enrollment Part- 150 161 194 505 Status Time Totals 502 358 445 13052) Events A and B have respective probabilities P(A) = 0.4 and P(B) = 0.5.You also know that P(A ∪ B) = 0.7.(a) What is P(A|B)?(b) What is P(B|A)?10 . Let A, B be independent events with P (A) = P (B) = 1/3. Find the probability that exactly one of the two will occur: Select one : a. 4/9 b. 1/9 c. 1/3 d. 2/9