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. Then, find the probability that you choose the same card twice.
A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 2 } { 9 }$
D) $\frac { 4 } { 9 }$

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. Then, find the probability that you choose the same card twice. 
A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 2 } { 9 }$
D) $\frac { 4 } { 9 }$

Quizplus · Accepted Answer

The sample space for choosing two cards with replacement from a set of three (King, Queen, Ace) includes all possible pairs: KK, KQ, KA, QK, QQ, QA, AK, AQ, AA. Since there are 9 possible outcomes and 3 of them involve choosing the same card twice (KK, QQ, AA), the probability of choosing the same card twice is $\frac{3}{9} = \frac{1}{3}$.

Solve the Problem 12\frac { 1 } { 2 }21​ B) 13\frac { 1 } { 3 }31​

Solve the Problem $\frac { 1 } { 2 }$ B) $\frac { 1 } { 3 }$