http://www.ck12.org Chapter 2. Conditional Probability
P(red and white) =2
9
×
6
17
P(red and white) =12
153
P(red and white) =4
51
If the first sock is white, willP(red and white) =P(white and red)as we found in Example 1? Let’s find out.
P(white) =6
18
P(white) =1
3
The probability of picking a red sock on the second pick is now:
As with the last example,P(red and white) =P(white and red). So when does orderreallymatter? We’ll find out in
the next concept.
Points to Consider
- How are tree diagrams helpful for determining probabilities?
Guided Practice
In a survey, baseball fans were asked who they would like to win the National League playoffs. 54% responded that
they would like the Phillies to win, and 46% responded that they would like the Giants to win. The fans were then
asked who they would like to win the American League playoffs if the Phillies win the National League playoffs,
and who they would like to win the American League playoffs if the Giants win the National League playoffs. If
the Phillies win the National League playoffs, 42% of the fans responded that they want the Rangers to win the
American League playoffs, and 58% said that they want the Yankees to win. If the Giants win the National League
playoffs, 48% of the fans responded that they want the Rangers to to win the American League Playoffs, and 52%
said that they want the Yankees to win. The results of the survey are shown in the following tree diagram: