6. Selecting a Jury. The grade appeal process at a university requires that a ju

Question

6. Selecting a Jury. The grade appeal process at a university requires that a jury be structured by selecting five individuals randomly from a pool of eight students and ten faculty a) What is the probability of selecting a jury of three students and two faculty? b) What is the probability of selecting a jury of one student and four factulty? c) What is the probability of selecting a jury of at least one student? 7. If two dice is rolled, find the probability of getting these results a) A sum of 7 or 11 b) A multiple of 6 c) Not getting doubles d) A sum greater than or equal to 10 8. In your community, 80% of the small businesses carry liability insurance or worker's compensation insurance. Forty percent carry liability insurance 50% of the small business carry worker's compensation insurance. If a small business is to be chosen at random, find the probability that the selected business carries both types of insurance. At the used-book sale, 100 books are adult books and 160 are children's books. Of the adult books, 70 are nonfiction while 97 of the children's books are fiction. If a book is selected at random, find the probability that it is 9. a) Fiction b) Not a children's nonfiction book. An adult book or a children's nonfiction book. c) d) Fiction given that it's a children's book 10. Suppose Jack draws marbles at random, without replacement, from a urn containing three red, two blue and five violet marbles. Find the following probability of a) 1st draw is Red and 2nd draw is blue 1st draw is Red and 2nd draw is violet and 3rd draw is violet. b) c) Getting at least one red ball if your draw three balls 11. At the Avonlea Country Club, 73% of the members play bridge and swim and 82% play bridge. If a member is selected at random, find the probability that the member swims, given that the member plays bridge. 12. According to the US Census Bureau, 80% of 16-to 24-year-olds are high school dropouts. In addition 21% of 16-to 24-year-olds are high school dropouts and unemployed. What is the probability that a randomly selected 16- to 24- year old is unemployed, given he or she is a dropout? 13. Children. A family has five children. If this family has exactly two boys, how many different birth and gender orders are possible? 14. In how many ways can the top 3 horses finish in a 15-horse race? 15, Suppose that a local area network requires six characters using letters and digits for usernames. The first character must be "K" or "W" and the last character must be a nonzero digit. How many user names are possible if same character cannot be used more than once? 87! 16. Simplity 82!5! A baseball team consists of three outfielders, four infielders, a pitcher, and a catcher. Assuming that the outfielders and infielders are indistinguishable, how many batting orders are possible? 17.

Explanation / Answer

8)
By addition rule ,
P(L or W) = P(L) + P(W) - P(L and W)
0.80 = 0.40 + 0.50 - P(L and W)
P(L and W) = 0.10

11)

Let A denote the event of playing bridge and B denote the event of playing swim.

p(A)= 82% or 82/100

p(AnB)= 73% or 73/100

p(B)=?

If A and B are independent events,
p(AnB)= p(A).p(B)
73/100=82/100.p(B)
73/82=p(B)
p(B)= 0.89

14)

we need to find top 3 horses = 15 *14 * 13
Number of ways = 2730

16)

87! / 82! * 5! = 36949857

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