2.7. Conditional Probability http://www.ck12.org
P(queen) =4
52
P(black ace) =2
51
P(black ace and queen) =4
52
×
2
51
P(black ace and queen) =8
2 , 652
P(black ace and queen) =2
663
Step 2:Calculate the probability of choosing black ace as a second card when a queen is chosen as a first card.
P(black ace|queen) =
P(black ace and queen)
P(queen)P(black ace|queen) =2
663
4
52
P(black ace|queen) =2
663
×
52
4
P(black ace|queen) =104
2 , 652
P(black ace|queen) =2
51
Step 3:Write your conclusion.
Therefore, the probability of selecting a black ace as the second card when a queen is chosen as the first card is 3.9%.
Example C
Sandra went out for her daily run. She goes on a path that has alternate routes to give her a variety of choices to
make her run more enjoyable. The path has 3 turns where she can go left or right at each turn. The probability of
turning right the first time is^12. Based on past runs, the probability of turning right the second time is^23. Draw a tree
diagram to represent the path. What is the probability that she will turn left the second time after turning right the
first time?