The prior probabilities for events A1 and Az are P(A1) = 0.50 and P(A2) = 0.50. It is also known that P(A1 n A2) = 0. SupposeP(B|A¡) = 0.10 and P(B|A2) = 0.70.a. Are events Aj and Az mutually exclusive?Select your answer -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)- Select your answer - Vb. Compute P(A1 n B) (to 2 decimals).Compute P(A2 n B) (to 2 decimals).c. Compute P(B) (to 2 decimals).d. Apply Bayes' theorem to compute P(A1|B) (to 4 decimals).Also apply Bayes' theorem to compute P(A2|B) (to 4 decimals).

Answered: Image /qna-images/answer/17e94c38-d008-49e9-b355-db6e6bc3ab98.jpg

Answered: The prior probabilities for events Aj…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose that, for events A and B, P(A)= 0.2, P(B)= 0.85, and P(AandB)= 0.17. Are A and B disjoint? Explain your answer in one or two sentences.
Suppose the probability of snow tomorrow is 0.4 while the probability of IU winning the basketball game tomorrow is 0.9. Assuming these events are independent, what is the probability that it snows and IU loses? (A) 1 (B) 0.04 (C) 0.06 (D) 0.4 (E) 0 (F) 0.54 (G) 0.36 (Н) 0.9 O B В C. O D O E OF OG
Results from trials for a new pill for sleeping are given in this table. slept better (B) no improvement (N) sleeping pill (S) 144 21 sugar tablet (T) 55 89 What is the probability that the subjects slept better if they took the sleeping pill = P(B|S) ? What is the probability that the subjects took the tablet if they slept better = P(T|B)? Give your answer as a fraction.
Q6: The probability that a person owns a microwave oven is 0.70, that a person owns a CD player is 0.26, and that person owns both a microwave and a CD player is 0.16, then the probability that a person owWns a microwave or a CD player is (A) 0.5 (B) 0.182 (C) 0.8 (D) None of the above
Suppose the probability of winning the Powerball lottery is 0.1, while the probability of being abducted by aliens is 0.6. If these two events are independent, what is the probability of winning Powerball but not being abducted? (A) 0.06 (B) 0.54 (C) 0.04 (D) 0.6 (E) 0 (F) 0.1 (G) 1 (H) 0.36
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).
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The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.45, the analogous probability for the second signal is 0.5, and the probability that he must stop at at least one of the two signals is 0.9. (a) What is the probability that he must stop at both signals? X (b) What is the probability that he must stop at the first signal but not at the second one? X (c) What is the probability that he must stop at exactly one signal?
Q. 2 The probability that a smoker who consumes over 20 cigarettes a day will suffer from chronic respiratory illness is 4 The 10 probability that he will suffer from heart disease is The 10 probability that he will suffer from at least one of these ailments is 6.5 10 (i) Find the probability that the smoker will suffer from both ailments. (ii) Find the probability that he will suffer from heart disease given that he suffers from chronic respiratory illness. (iii) Find the probability that he will suffer from chronic respiratory illness given that he suffers from heart disease. (iv) Are events "chronic respiratory illness" and "heart disease independent"?
The prior probabilities for events A, and Az are P(A1) = 0.40 and P(A2) = 0.60. It is also known that P(A, n A2)=0. Suppose P(B|A1) = 0.10 and P(B|A2) = 0.20. a. Are events A1 and Ag mutually exclusive? Select your answer- 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) - Select your ans wer - ♥ b. Compute P(A1N B) (to 2 decimals). Compute P(A2 nB) (to 2 decimals). C. Compute P(B) (to 2 decimals). Apply Bayes' theorem to compute P(A1 B) (to 4 decimals). Also apply Bayes' theorem to compute P(A2|B) (to 4 decimals).
q15A -
Let A be the event that a flight from New York to San Fransisco arrives on time and let B be the event that it is a clear day in San Fransisco. Suppose that the probability of a clear day is P(B)=0.6.and the probability a plane arrives on time is P(A)=0.7. We also know that the probability a plane arrives on time on a cloudy day is P(A|B^C)=0.5, The events A and B are? Dependent Events Independent Events Disjoint Events All of the Above

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