2.1. Tree Diagrams http://www.ck12.org
Irvin puts the sock back in the drawer and pulls out the second sock. The probability of getting a white sock on the
second draw is:
P(white) =6
18
P(white) =1
3
Therefore, the probability of getting a red sock and then a white sock when the first sock isreplacedis:
P(red and white) =2
9
×
1
3
P(red and white) =2
27
One important part of these types of problems is that order is not important.
Let’s say Irvin picked out a white sock, replaced it, and then picked out a red sock. Calculate this probability.
P(white and red) =1
3
×
2
9
P(white and red) =2
27
So regardless of the order in which he takes the socks out, the probability is the same. In other words,P(red and white) =
P(white and red).
Example C
In Example B, what happens if the first sock isnot replaced?
The probability that the first sock is red is:
P(red) =4
18
P(red) =2
9
The probability of picking a white sock on the second pick is now:
So now, the probability of selecting a red sock and then a white sock, without replacement, is: