Solve the problem.
-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) $K Q , K A , Q K , Q A , A K , A Q$
B) $\mathrm { KK } , \mathrm { KQ } , \mathrm { KA } , \mathrm { Q } Q , \mathrm { Q } A , \mathrm { AQ } , \mathrm { A } \mathrm { A }$
C) $\mathrm { KK } , \mathrm { KQ } , \mathrm { KA } , \mathrm { QK } , \mathrm { Q } Q , \mathrm { Q } \mathrm { A } , \mathrm { A } \mathrm { K } , \mathrm { A } Q , \mathrm {~A} \mathrm {~A}$
D) $\mathrm { K } \mathrm { KQ } , \mathrm { KAK } , \mathrm { QQQ } , \mathrm { KQ } , \mathrm { AA } \mathrm { K }$

Question

Solve the problem.
-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) $K Q , K A , Q K , Q A , A K , A Q$
B) $\mathrm { KK } , \mathrm { KQ } , \mathrm { KA } , \mathrm { Q } Q , \mathrm { Q } A , \mathrm { AQ } , \mathrm { A } \mathrm { A }$
C) $\mathrm { KK } , \mathrm { KQ } , \mathrm { KA } , \mathrm { QK } , \mathrm { Q } Q , \mathrm { Q } \mathrm { A } , \mathrm { A } \mathrm { K } , \mathrm { A } Q , \mathrm {~A} \mathrm {~A}$
D) $\mathrm { K } \mathrm { KQ } , \mathrm { KAK } , \mathrm { QQQ } , \mathrm { KQ } , \mathrm { AA } \mathrm { K }$

Quizplus · Accepted Answer

Since the selection is with replacement, each draw is independent, and all combinations of the cards drawn are possible, including drawing the same card twice. This results in 9 possible outcomes: KK, KQ, KA, QK, QQ, QA, AK, AQ, AA.

Solve the Problem KQ,KA,QK,QA,AK,AQK Q , K A , Q K , Q A , A K , A QKQ,KA,QK,QA,AK,AQ

Solve the Problem $K Q , K A , Q K , Q A , A K , A Q$