The following table shows the results of a survey of authors by a (fictitious) publishing company. HINT [See Example 5.] Successful Unsuccessful Total New Authors 5 17 22 Established Authors Find the number of elements it contains. authors 23 55 78 Total 28 72 100 Consider the following events: S: an author is successful; U: an author is unsuccessful; N: an author is new; and E: an author is established Describe the event U U E' in words. O This is the event that an author is either successful or not established. O This is the event that an author is either successful or established. This is the event that an author is unsuccessful and established. O This is the event that an author is either unsuccessful or not established. O This is the event that an author is unsuccessful and not established.

One student is selected at random. Let's define the following events:A = event the student selected is under 21,B = event the student selected is over 30,C = event the student selected is in his or her 20s, andD = event the student selected is over 18.1. Determine the following events.a. E=(not D) b. F=(A & D) c. G= (A or D) d. H= (B or C)   Please help me with the below  1) Using the data in the table, calculate the probabilities of these events: A,B,C,D,E,F,G and H. 2. We consider tossing a coin four times:a. How many outcomes this experiment has? b. Draw the tree diagram

A poll of 120 city residents found that 30 had visited the new museum, and that 80 had been to the new park. If it appeared that going to the park and going to the museum were independent events, how many of those polled had been to both? Park O 20 O 15 Museum Yes No Total Hint: P(went to park and went to museum) divided by total people surveyed O 10 Yes ?? No 80 40 Total 30 90 120 OIt cannot be determined.

pleaseeeee solve question 3, quickly please

d. Are events A and C mutually exclusive? - Select your answer - e. What is Bº? (i) {E1, E3, E5, E6} (ii) {E2, E4, E5, E7} (iii) {E3, E4, E5, Es} (iv) {E₁, E4, E6} (v) {E2, E4, E7} (vi) {0} - Select your answer - What is P(B)? If necessary round your answer to two deicmal places.

Please answer the question and explain fully.

4. 60% of homeowners in Northern Virginia have a weekly lawn service. Those homes with a lawn service, 55% have a sprinkler system. For those without a lawn service, 30% have a sprinkler system. (Note: you do NOT need to simplify these answers. However, you MUST express each in terms of the events/probability notation – e.g., P(A|B) =..) a. Draw a tree diagram to model the problem b. What is the probability that a randomly selected home has a sprinkler system? c. What is the probability that a randomly selected home with a sprinkler system has a lawn service? d. What is the probability that a randomly selected home with a lawn service has a sprinkler system? e. What is the probability that a randomly selected home has a lawn service? f. What is the probability that a randomly selected home that does not have a lawn service has a sprinkler system?