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), K (king) of that suit. Three cards are picked at random.

a. Suppose you know that the picked cards are Q of spades, K of hearts and Q of spades. Can you decide if the sampling was with or without replacement?

b. Suppose you know that the picked cards are Q of spades, K of hearts, and J of spades. Can you decide if the sampling was with or without replacement?

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

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.

• In 1st case when we get Q of spades, K of hearts and Q of spades - As we get Q of spades twice, & there is single card of this in the deck. It means that sample must have been chosen with replacement.
• In 2nd case Q of spades, K of hearts, and J of spades - As all drawn cards are different, the sample could have drawn with or without replacement.