Probability

11. In a large population, 60% of the people have been vaccinated. If 4 people are randomly selected, what is the probability that at least one of them has been vaccinated? Give your answer as a decimal to 4 places.

8. The table lists the smoking habits of a group of 400 college students

9. There are 10 cans of fruit juice left in a bowl, 3 of apple juice (A), 5 of orange juice (O), and 2 of grape juice (G). You reach into the container and randomly select two cans in succession. Find the probability of: (i) selecting two cans of apple juice (b) 15 (a) 2 45 (ii) Selecting no cans of apple juice (a) 7 15 (b) (iii) Selecting one can of apple juice 7 30 3 10 (b) (c) 3 50 (c) 0 15 15 100 (d) None of the above (d) None of the above

10. The data from a survey of 140 students showed that 37 study music, 98 play a sport and 25 do neither. (1) Create a Venn diagram to illustrate the data collected. Let M = music, S = sport (ii) If a student is selected at random, what is the probability that he or she will study music and play a sport 23 28 ê (b) 28 49 (©) } // (d) 0 (iii) What is the probability that a randomly selected student will study music given that he/she plays a sport. (a) 0.1429 5 (c) (d) 0.2643 (e) none of these 28 (e) none of these

What is the empirical probability that a randomly selected female superhero will have telepathy?s

Question 2 (1 point) A spinner is broken into sections labeled 1 to 40. What is the probability that, on your next spin, that you will spin a number less than 3?

What is the empirical probability that a randomly selected superhero will have super strength?

Question 3. Diagnostic and serology tests are crucial tools to fight the spread of severe acute respiratory syndrome coronavirus such as Convid-19. Unfortunately, tests are not 100% reliable you may test positive and not be sick this is called a false positive; you may test negative when you are sick - this is called a false negative. We can formulate these types of problems in in terms of conditional probabilities: For the following questions consider the following information provided to us by the kit manufacturer

Question 1. To study the physical fitness of a sample of GWU Students the data below was collected representing the number of sit-ups (x) that a student could do in one minute.

Question 2. A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. a) What is the probability that all of them are red? b) What is the probability that we get one