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a bag contains articles of 4 different kinds-periodical,novel,newspaper,hardcover.WHAT...
a bag contains articles of 4 different kinds-periodical,novel,newspaper,hardcover.WHAT IS THE SMALLEST NUMBER OF ARTICLES IN THE BAG SATISFYING FOLLOWING CONDITIONS
when 4 articles are drawn from the bag without replacement the following events are equally likely-
1. the selection of 4 periodicals.
2. the selection of 1 novel and 3 periodicles
3. the selection of 1 news paper.1 novel & 2 periodicles
4. the selection of 1 article of each kind
WHAT IS THE SMALLEST NUMBER OF ARTICLES IN THE BAG SATISFYING THESE CONDITIONS?HOW MANY OF THESE ARE OF EACH KIND?
5 Answers | add yours
- 1 news article
- 1 novel
- 4 periodicals
- 4 news papers
- 4 novels
- 1 news paper and 3 novels
- 1 news paper and 3 periodicals
- 2 news papers and 2 novels
- 3 news papers and 1 novel
- 3 news papers and 1 periodical
- 3 novels and 1 periodical
- 2 news papers and 2 periodicals
- 2 novels and 2 periodicals
- 1 news paper, 2 novels and 1 periodical
- 2 news papers, 1 novel and 1 periodical
- 1 newspaper
- 1 novel
- 1 hardback
- 4 periodicals
- result (4) selection of one of each (includes the hardback)
- result (1) selection of 4 periodicals
- result (3) selection of 1 newspaper, 1 novel, and 2 periodicals
- result (2) selection of 1 novel and 3 periodicals.
The smallest number of articles is 16, 4 of each kind.
Posted by michaelpaulheart on February 16, 2012 at 5:29 PM (Answer #1)
can you please explain
Posted by mubashirak on February 17, 2012 at 3:54 AM (Answer #2)
Valedictorian, Super Tutor, Tutor
Yes, an explanation would be the meat of the correspondance.
Posted by etotheeyepi on February 17, 2012 at 4:20 AM (Answer #3)
The key condition determinate of the answer above is "equally" likely: 1:16 probability.
An unequal probability--yielding exclusively any one of the four desired results once--would obtain from a smaller number of articles in the bag (6):
1:4 probability, the number of possible combinations listed in the question equal to the number of possible draws from the bag.
Note that the original question did not include the conditional "exclusively"--"What is the smallest number of articles in the bag satisfying these conditions exclusively?"--admitting of additional possibilities.
Therefore--Included in the answer is the additional possibility of drawing:
Add to these 12 (unexcluded possibilities) the 4 possibilities proposed in the question and the probability of drawing any one of the 4 originally proposed combinations is demonstrated to be 1:16.
Posted by michaelpaulheart on February 21, 2012 at 12:09 AM (Answer #4)
My apology: I did not advert to the "hardcover" article in the original proposed question.
The absolute minimum number of articles necessary for an unequal probability of any one of the 4 possible results proposed in the original question requires (7):
In the original question the probability of results (2) and (3) is > probability of results (1) and (4), with the probability of result (1) > (4) under the conditions listed immediately above.
Increasing order of probability then in that case seems to me to be:
The probability of a selection having a larger number of periodicals than 1 is greater than the probability of 1 of each of the 4 articles or the probability of 4 periodicals only, due to the greater number of the periodicals 4:1 each or 4:3 collectively in the bag.
But this unequal probability is removed with the inclusion of the same number of newspapers, of novels, of hardbacks as the number of periodicals. Hence, the minimum number of articles providing the equal probability of each of the 4 possible selections listed in the original question is 16, 4 of each.
Posted by michaelpaulheart on February 21, 2012 at 6:13 AM (Answer #5)
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