13. A has chance obtaining a degree from each category listed below. Draw a tree
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13. A has chance obtaining a degree from each category listed below. Draw a tree diagram showing all possible ways a person could obtain these degrees. S Doctor's Bachelor's Master Ph.D M.S D.Ed M.Ed B.A. MA 14. A television news director wishes to use three news stories on an evening show. One story will be the "lead story," one will be the second story, and the last will be a "closing story." If the director has a total of eight stories to choose from, how many possible ways can the program are set up 15. There are seven women and five men in department. How many ways can a committee of four people are selected? How many ways can this committee are selected if there must be two men and two women on the committee? How many ways can this committee are selected if there must be at least two women on the committee? 16. If one card is drawn from an ordinary deck of cards, find the probability of getting the following (a) A club or a heart or a diamond. (b) A king or a queen or a heart. (c) An ace or a diamond or a club 17. An automobile manufacturer has three factories, A, B, and C. They produce 40% 33%, and 27%, respectively, ofa specific model of car. Fifty-five percent of the cars produced in factory A are white, 41% ofthose produced in factory B are white, and 36% produce in factory Care white. Draw a tree diagram. If an automobile produced by the company is selected at random, find the probability that it is white 18. Eighty students in a school cafeteria were asked if they favored a ban on smoking in the cafeteria. The results of the survey are shown in the table. Class No opinion Favor Oppose 15 27 8 Freshman 23 2 Sophomore If a student is selected at random, find these probabilities. (a) Given that the student is a freshman, he or she opposes the ban (b) Given that the student favors the ban, the student is a sophomore.Explanation / Answer
14. Since here the order of the story matters i.e First is the lead story then the second story and in last the closing story, hence we will use permutations. We have to choose 3 stories from the available 8. Thus,
8P3 = 8! / 5! = 336.
15. i) There are total 7+5 = 12 people. We have to choose a committee of 4 people. Hence the total number of possible ways are C(12,4) = 12! / 4! 8! = 495.
ii) Now if there are 2 men and 2 women then there are
C(7,2) * C(5,2) = 210 ways to form committee.
iii) Now if there has to atleast 2 women in the committe then
C(7,2) * C(5,2) + C(7,3) * C(5,1) + C(7,4) = 420 ways
16. a) A club or a heart or a diamond
P(Getting a club) = 13/52
P(Getting a heart) = 13/52
P(Getting a diamond) = 13/52
P(Getting a club or a heart or a diamond) = 13/52 + 13/52 + 13/52 = 39/52 = 0.75
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