How to Work Out a Tree Diagram Without Replacement
In mathematics, probability describes the likelihood of an event. An experiment is a process or investigation and an outcome is a possible result of an experiment. The sample space is the set of all possible outcomes. The sample space may change for the different events in a multi-step experiment. For example, if you draw two cards from a deck of playing cards without replacing the first card, the sample space for the first event is 52 cards, but the sample space for the second event is only 51 cards. One way to visually represent probability is with a tree diagram, which consists of lines, or branches, for each possible outcome of the experiment.
Other People Are Reading
Instructions
-
-
1
Draw a tree diagram to represent the experiment. For example, find the probability that two random cards drawn from a deck of cards without replacement are both aces. From a single point, draw branch (a) of the tree diagram to represent the outcome that the first card is an ace. Label the branch with the probability, which is 4/52, or 1/13 in simplest form.
-
2
From the same point, draw branch (b) to represent the outcome that the first card is not an ace. Label the branch with the probability, which is 48/52, or 12/13 in simplest form.
-
-
3
Start at the end of branch (a) and draw branch (c) to represent the outcome that the second card is an ace. Label the branch with the probability, which is 3/51.
-
4
Start at the end of branch (a) and draw branch (d) to represent the outcome that the second card is not an ace. Label the branch with the probability, which is 48/51.
-
5
Start at the end of branch (b) and draw branch (e) to represent the outcome that the second card is an ace. Label the branch with the probability, which is 3/51.
-
6
Start at the end of branch (b) and draw branch (f) to represent the outcome that the second card is not an ace. Label the branch with the probability, which is 48/51.
-
7
Multiply the probability from branch (a) by the probability from branch (c) to find the probability both cards are aces: 1/13 --- 3/51 = 3/663, or 1/221 in simplest form.
-
1
Tips & Warnings
Use a straightedge to draw your branches on the tree diagram.
Clearly label your diagram.
References
Resources
- Photo Credit ruler and pencil image by Stepanov from Fotolia.com
