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Chapter 3: Q3.5 (page 182)

You have a fair, well-shuffled deck of 52 cards. It consists of four suits. The suits are clubs, diamonds, hearts, and spades. There are 13 cards in each suit consisting of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), and K (king) of that suit. S = spades, H = Hearts, D = Diamonds, C = Clubs. Suppose that you sample four cards without replacement.

Which of the following outcomes are possible? Answer the same question for sampling with replacement.

a. QS, 1D, 1C, QD

b. KH, 7D, 6D, KH

c. QS, 7D, 6D, KS

Short Answer

Expert verified

a) QS, 1D, 1C, QD and c) QS, 7D, 6D, KS : outcomes are possible without replacement. All a), b) & c) are possible with replacement.

Step by step solution

01

Basics 

Deck of 52 cards include following cards

  • Spade 1, spade 2, spade 3, spade 4, spade 5, spade 6, spade 7, spade 8, spade 9, spade 10, spade Jack, spade queen, spade king
  • clubs 1, club 2, club 3, club 4, club 5, club 6, club 7, club 8, club 9, club 10, club Jack, club queen, club king
  • diamond 1, diamonds 2, diamond 3, diamond 4, diamond 5, diamond 6, diamond 7, diamond 8, diamond 9, diamond 10, diamond Jack, diamonds queen, diamond king
  • heart 1, heart 2, heart 3, heart 4, heart 5, heart 6, heart 7, heart 8, heart 9, heart 10, heart Jack, heart queen, heart king
02

Explanation 

Sample picking with replacement means that after picking a sample, selected unit is again returned back to the set, before the next sample is picked.

Sample picking without replacement means that after picking a sample, selected unit is not again returned back to the set, before the next sample is picked.

a) QS, 1D, 1C, QD : As all cards are different, so it can be possible with & without replacement

b) KH, 7D, 6D, KH : There is only single king heart in the deck, getting heart kings twice means that the sample is with replacement. So, it can't be possible without replacement.

c) QS, 7D, 6D, KS : As all cards are different, so it can be possible with & without replacement

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Most popular questions from this chapter

Table 3.6shows a random sample of 200cyclists and the routes they prefer. Let M= males and H= hilly path.

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Use the following information to answer the next ten exercises. Forty-eight percent of all Californians registered voters prefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55%prefer life in prison without parole over the death penalty for a person convicted of first degree murder. 37.6%of all Californians are Latino. In this problem, let: 鈥� C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder. L = Latino Californians. Suppose that one Californian is randomly selected.

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A shelf holds 12books. Eight are fiction and the rest are nonfiction. Each is a different book with a unique title. The fiction books are numbered one to eight. The nonfiction books are numbered one to four. Randomly select one book

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What is the sample space?

Forty-eight percent of all Californians registered voters prefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55%prefer life in prison without parole over the death penalty for a person convicted of first degree murder. 37.6%of all Californians are Latino. In this problem, let: 鈥� C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder. L = Latino Californians. Suppose that one Californian is randomly selected.

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See all solutions

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