Question

question 12
there are 3 cards in a hat: one is a king, one is a queen, and one is an ace. two cards are to be selected at random with replacement. using a tree diagram, obtain the sample space for the experiment. list the elements that make up the sample space.
a kq, ka, qk, qa, ak, aq
b kk, kq, ka, qq, qa, aq, aa
c kk, kq, ka, qk, qq, qa, ak, aq, aa
d kkq, kak, qqq, kq, aak
4 points

Explanation:

Step1: Analyze the composition of each option

We need to check if each option has one king (K), one queen (Q), and one ace (A).

• Option A: KQ, KA, QK, QA, AK, AQ. Each combination has one K, one Q, and one A.
• Option B: KK, KQ, KA, QQ, QA, AQ. Here, KK has two Ks and no A in the first element, QQ has two Qs and no A in the fourth element.
• Option C: KK, KQ, KA, QK, QQ, QA, AK, AQ, AA. KK has two Ks, QQ has two Qs, AA has two As.
• Option D: KKQ, KAK, QQQ, KQ, AAK. KKQ has two Ks, KAK has two Ks, QQQ has three Qs, AAK has two As.

Answer:

A. KQ, KA, QK, QA, AK, AQ