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 a king and a queen are selected.
A) $\frac { 4 } { 9 }$
B) $\frac { 2 } { 9 }$
C) $\frac { 2 } { 3 }$
D) $\frac { 1 } { 3 }$

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 a king and a queen are selected. 
A) $\frac { 4 } { 9 }$
B) $\frac { 2 } { 9 }$
C) $\frac { 2 } { 3 }$
D) $\frac { 1 } { 3 }$

Quizplus · Accepted Answer

The sample space for selecting 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 selections are with replacement, each draw is independent, and the probability of drawing any specific card is $\frac{1}{3}$. The probability of selecting a King and then a Queen or a Queen and then a King is $\frac{1}{3} \times \frac{1}{3} + \frac{1}{3} \times \frac{1}{3} = \frac{2}{9}$.

Solve the Problem 49\frac { 4 } { 9 }94​ B) 29\frac { 2 } { 9 }92​

Solve the Problem $\frac { 4 } { 9 }$ B) $\frac { 2 } { 9 }$