Example 3.5 from Statistics, 3.2 Independent and Mutually Exclusive Events

Independent and Mutually Exclusive Events: example 3.5

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 you pick four cards, but do not put any cards back into the deck. Your cards are QS, 1D, 1C, QD.
Suppose you pick four cards and put each card back before you pick the next card. Your cards are KH, 7D, 6D, KH.

Which of a. or b. did you sample with replacement and which did you sample without replacement?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
a. Because you do not put any cards back, the deck changes after each draw. These events are dependent, and this is sampling without replacement; b. Because you put each card back before picking the next one, the deck never changes. These events are independent, so this is sampling with replacement.

How did it go?

Solution

Solution