Question

The jack, queen, king, and ace of diamonds are removed from a standard deck of cards. One card is selected at random from these four cards, returened to the deck, and then another is selected. a. illustrate the outcomes using a list, a tree diagram, or a chart. b. repeat with repetition of cards not permitted. c. Explain the difference in the resulting number of outcomes.

Answer 1

Let J, Q K and A indicate jack, queen, king and ace respectively

a) When two cards are drawn with replacement, the possible outcomes are given in the sample set below:

Sample space = {JJ, JQ, JK, JA, QJ, QQ, QK, QA, KJ, KQ, KK, KA, AJ, AQ, AK, AA}

b) If repetition is not allowed,

Sample space = {JQ, JK, JA, QJ, QK, QA, KJ, KQ, KA, AJ, AQ, AK}

c) In first case, there are 4 possible outcomes in each trial. So, number of outcomes = 4 x 4 = 16

When repetition is not allowed, after first card is drawn, number of cards remaining for second draw = 3

Therefore, number of outcomes possible = 4 x 3 = 12

The difference in number of outcomes is because the number of outcomes for second trial is only 3 if repetition is not allowed.