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|A Tree Diagram and Sample Space
A tree diagram is a graphic representation of the step by step competion of an experiment showing all possible results of each step. It is generally drawn from a starting point on the left and then branches to the right with each possilbe outcome shown as the end of the next branch or bridge.
A sample space is a list of all the results of the experiment.
The sample space may be found by following each path on the tree diagram starting on the left and moving to the last event on the right.
At the left, the tree diagram and sample space for the experiment "flip 3 coins" is shown.
The tree and results for the flip of the first coin, Heads or Tails, is shown in blue.
The tree and results for the second flip of a coin are shown in red. Note that for each branch from the blue tree, either a Heads or a Tails is shown in red.
The tree and results for the third flip of a coin are shown in purple.
The sample space is shown in green and each path from left to right on the tree results in a possilbe result of the experiment "flip 2 coins."
1. From the bag containing a blue, a red, a green, and an orange ball, draw a first ball then a second ball without replacement.
In the above example, order counts -- there's a first ball and a second ball.
In the next example, order does not count -- there's now way to tell the first ball from the second ball.
2. From the bag containing a blue, a red, a green, and an orange ball, draw two ball without replacement from a bag containing a blue, a red, a green, and an orange ball.List the sample space. Remember not to list duplicates.
4. Select a color from red, white, and blue, then select a number for 2 and 3, then select the other number.
|5. Toss a coin, then select a color from red, white, and blue, then pick the number 2 or the number 4.|
6. Flip a coin, roll a die.
7. Ann, Martin, Nancy, and Tom are in a club of 4 members. They must choose a president, secretary, and treasurer.
|8. Toss Coins
Choose a ham or roast beef sandwhich. Choose coffee, tea, or soda. Choose ice cream or apple pie.