Suppose that A and B are non-mutually exclusive events such that 17 . P(A) = 21,P(B) = 2121 and P(A or B) = Show this situation using the Venn diagram. 21
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- Suppose A and B are two events. If P(A)=0.5, P(B)=0.4, and P(AUB)=0.8. Then find the ? P(AN B) None of these .A 0.4 .B 0.0.C 0.3.D https://mood e IT:E9 ENG ) G TOSHIBA 40 BVD CIVB 247 23 3r 24 & 48 50 67 7V 8A 99 DI F1 GY V BY NIThe events E and T, are defined as E = the event that someone who is out of work and actively looking for work will find a job within the next month and T = the event that someone who is currently out of work has been out of work for i months. For example, T, is the event that someone who is out of work has been out of work for 2 months. The following conditional probabilities are approximate and were read from a graph in a paper. P(E|T,) = 0.29 P(E|T3) = 0.21 P(E|T5) = 0.19 P(E|T,) = 0.18 P(E|T,) = 0.17 P(E|T11) = 0.17 P(E|T,) = 0.28 P(E|T) = 0.20 P(E|T) = 0.18 P(E|TR) = 0.17 P(E|T10) = 0.17 P(E|T,2) = 0.17 (a) Interpret the following two probabilities. (1) P(E|T,) = 0.29 O This is the probability that a person who has been out of work for a month will find work within the next month. O This is the probability that a person who has been out of work for three months will find work within the next three months. O This is the probability that a person who has been out of work for six…The probability that Taylor Swift is Austin’s favorite music artist is .10. The probability that he will go to one of her concerts is .84. However, the probability that he does not like Taylor Swift and will go to a concert (because his wife makes him) is .75. a.) Write down the 3 pieces of information given in terms of probabilities involving event A (Taylor Swift is Austin’s favorite music artist) and event B (Austin will go to a Taylor Swift concert). b.) Summarize the above information using a probability table. c.) Find the probability that Taylor Swift is Austin’s favorite music artist or Austin will go to a Taylor Swift concert.
- 2. Let A be the event that you read a book before bed, let B be the event that you will check Instagram before bed, and let C be the event that you brush your teeth right before going to bed. Express the following event in symbols: Either you will brush your teeth or check Instagram before going to bed, but you will not read a book right before bed.13.Example 3-28. Let P (A) = p, P (A \B) = q, P (B | A) = r. Find relations betwe number p, q, r for the following cases : (a) Events A and B are mutually exclusive. (b) A and B are mutually exclusive and collectively exhaustive. (c) A is sub-event of B ; B is a sub-event of A. (d) Ā andB are mutually exclusive.
- 3. The following is called the Bonferroni's inequality: For events A and B, we have that: P(ANB) ≥ P(A) + P(B) – 1. - a. Prove the Bonferroni inequality. b. Let A and B be events with probabilities P(A) Show that ≤P(AΜB) ≤ } . 12 = 3 and P(B) = 3.Suppose that C and D are two events such that Upper P left parenthesis Upper C right parenthesisequalsone half and Upper P left parenthesis Upper C & Upper D right parenthesisequalsone tenth. What is Upper P left parenthesis DIC right parenthesis?