Question

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

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

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

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