A friend of mine is giving a dinner party. His current wine supply includes 12 b
ID: 3353638 • Letter: A
Question
A friend of mine is giving a dinner party. His current wine supply includes 12 bottles of zinfandel, 10 of merlot, and 8 of caberne (he only drinks red wine), all from different wineries (a) If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) If 6 bottles of wine are to be randomly selected from the 30 for serving, how many ways are there to do this ways (c) If 6 bottles are randomly selected, how many ways are there to obtaln two bottles of each varlety? ways (d) If 6 bottles are randomly selected, what Is the probability that this results In two bottles of each varlety belng chosen? (Round your answer to three decimal places.) (e) If 6 bottles are randomly selected, what is the probabilty that all of them are the same variety? (Round your answer to three decimal places.) Need Help? Read It Taik to a Tutor 6, 0.12 points Devresiat9 2 E 035 A production facility employs 10 workers on the day shift, 8 workers on the swing shift, and 6 workers on the graveyard shift. A quality control consultant is to select 6 of these workers for in-depth interviews. Suppose the selecti being selected as does any other group (drawing 6 slips without replacement from among 24) ()How many selections resul in all 6 workers coming from the day shift? What is the probability that al6 selected workers wll b from the day (Rond your answer to four decimal places.) (b) What is the probability that all 6 selected warkers will be from the same shift? (Round your answer to four decimal places selections (c) What is the probability that at least two different shifts will be represented among the selected workers? (Round your answer to four decimal places.) (d) What is the probability that at least one of the shifts will be unrepresented in the sample of workers? (Round your answer to four decimal places.) Need Help? iTalk to s TutorExplanation / Answer
1)
a)
since serving order is important,so we select 3 bottles from 12 and arrange them in 12P3 ways =1320
b) number of ways =30C6 =593775
c) number of ways =12C2 * 10C2 * 8C2 =66*45*28 =83160
d) probability =( 12C2 * 10C2 * 8C2 )/ 30C6 = 83160/593775 =0.140
e) probability =(selecting 6 from 12 bottles or selecting 6 from 10 or selecting 6 from 8 ) /(selecting 6 from 30 bottles)
= (12C6 +10C6 +8C6)/30C6
=(924+210+28)/593775
=1162/593775
= 0.002
2)
a) number of selections =24C6 =134596
b) Prob =n(selecting 6 from 10 or selecting 6 from 8 or selecting 6 from 6)/n(selecting 6 from 24)
= (10C6 +8C6 + 6C6 )/(24C6)
=(210+28+1)/134596
=239/134596
=0.0018
c) Prob(atleast 2 shifts) =1-P( only one shift)
= 1- 0.0018
=0.9982
d) P(atleast one shift is unrepresented) = (18C6 +14C6 +16C6 -10C6 -8C6 -6C6)/(24C6
=(18564+3003+8008-210-28-1)/134596
=(29336/134596)
=0.2180