2. From a group of 12 people, what is the probability that: a) none share a birthday b) at least two of them share the same birthday?
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- Suppose you have a class with 30 students ‒ 10 freshmen, 12 sophomores, and 8 juniors. a) You pick one student at random. What is the probability that the student is not a junior? b) You pick two students at random, one at a time. What is the probability that both are freshmen? c) You pick two students at random, one at a time. What is the probability that the second student is a freshman, given that the first is a freshman?8. In a class of 16 students, 4 are undergrads. For the final project, students are randomly divided into 4 groups. a. What is probability that each group has only 1 undergrad, if the groups are of equal size? b. What is the probability that each group has I undergrad, if groups have at least1 student?20. In a survey of 400 households, 360 said they own a VCR, 170 said they own a DVD player and 19 said they didn't own either. If a person is selected at random from this survey, what is the probability that the person: a) owns a VCR, a DVD player or both? b) owns both a VCR and a DVD player? c) only owns a DVD player?
- a group of 200 students includes 120 who watch television news, 80 who read a newspaper, and 60 who watch television and read a newspaper. if a student is selected at random, find the probability that the student will a) watch television news or read a newspaper? b) neither watch television news nor read a newspaper? c) only watch television news? d) only read a newspaper?What is the probability that in a group of n people at least two of them will have the same birthday. Leap year is excluded.13. In a family with three children, find the probability of having: a. exactly 3 girls b. at most 2 boys c. at least 1 girl
- A college surveys the 1258 alumni from 2019 and 2020. Of the 679 alumni from 2019, 127 went on to graduate school. Of the 579 alumni from 2020, 196 went on to graduate school. Find the probability that an alumnus selected at random from 2019 and 2020 is as described. a) a 2019 alumnus? b) a 2020 alumnus? c) a 2019 alumnus who did not attend graduate school?3. On Wednesday afternoons, eight men play tennis on two courts. They know ahead of time which four will play on the north court and which four will play on the south court. The payers arrive randomly at the tennis courts. What is the probability that the first four players that arrive are all assigned to a) the north court? b) the same court?of the 300 grade 10 students of a certain high school, 120 joined mathematics club, 115 joined science club and 100 joined english club. furthermore, 55 joined mathematics and science club, 50 joined mathematics and english club and 40 joined science and english club. finally, 80 students did not join any of these clubs. if a student is selected from this group, find the probability that the chosen student joined. a) all the three clubs. b) mathematics or the english club. c) any of the three clubs d) science club only. e) mathematics and science club but not english club.
- 10. If the probability that an item is defective is 0.08, what is the probability that among 8 such items: a) At most two will be defective? b) At least four will be defective?Please4) In Toronto, Canada, 55% of people pass the drivers’ road test. Suppose that 100 people take the test. d) What is the probability that at least 49 passed? e) What is the probability that at most 45 passed?