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Probability Tree Diagrams Explained

This document discusses probability through examples of drawing items from boxes with replacement and without replacement. For the first problem of drawing 3 items without replacement from a box with 3 hats, 3 bowties, and 3 fish, the document lists all 27 possible outcomes and their probabilities. For the second problem of drawing 3 items with replacement from a box with 3 red hearts, 3 pink hearts, and 3 yellow hearts, the document similarly lists the 27 possible outcomes and their equal probabilities of 27/729.

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237 views8 pages

Probability Tree Diagrams Explained

This document discusses probability through examples of drawing items from boxes with replacement and without replacement. For the first problem of drawing 3 items without replacement from a box with 3 hats, 3 bowties, and 3 fish, the document lists all 27 possible outcomes and their probabilities. For the second problem of drawing 3 items with replacement from a box with 3 red hearts, 3 pink hearts, and 3 yellow hearts, the document similarly lists the 27 possible outcomes and their equal probabilities of 27/729.

Uploaded by

api-425358907
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Thing 1 and Thing 2 Love’s

Provability Trees
Probability:

Is the probability of something happening in the future.

Start with a experiment:

Activity whose result can be observe and record.

Outcomes:

All possible results

Sample pace:

A set of all possible outcomes for an experiment.

Tree diagram:

Modeling tree example

Event subset of the sample spaces:

P € ----- something to occur

P (s)---- simple size


There are two set of problem of how we can used probability one can be done
with replacement or it can be done without replacement.

Problem #1

There are 9 items in a toy box - 3 are hats, 3 are bowtie and the other 3 are fish.
Given three drawings what are the possible outcomes and the probability
percent of each drawing.

3 hats

3 bowtie

3 fish

Each box has all the 9 toys in different boxes.

3 hats 3 bowtie 3 fish

This way is easier to recognize each item that is in the box.

The next thing we are going to do is to put the tree diagram and fill it in.
Tree diagram
With no replacement
Continue
bowtie 1/7
bowtie 2/8 hat 3/7
fish 3/7
bowtie 2/7
bowtie 3/9 hat 3/8 hat 2/7
fish 3/7
bowtie 2 /7
fish 3/8 hat 3/7
fish 2/7
bowtie 2/7
hats 2/7
bowtie 3/8
fish 3/7
bowtie 3/9
bowtie 3/7
hats 3/9 hats 3/9 hats 2/8
hats 1/7
fish 3/9 fish 3/7
bowtie 3/7
fish 3/8 hats 2/7
fish 2/7
bowtie 3/7
hat 3/8 hats 2/7
fish 2/7
fish 3/9 bowtie 2/7
bowtie 3/8 hats 3/7
fish2/7
bowtie 3/7
fish 2/8 hats 3/7
fish 1/7
Outcomes

1. BBB 3/9 X 2/8 X 1/7 = 6/ 504 16.HFB 3/9 x 3/ 8x 3/7 =27/504


2. BBH 3/9 x 2/8 x 3/7 = 18 / 504 17.HFH 3/9 x 3/8 x 2/7 = 18/ 504
3. BBF 3/9 x 2/8 x3/7 = 18/504 18.HFF 3/9 x 3/8 x 2/7 =18 /504
4. BHB 3/9 x 3/8 x 2/7 = 18/504 19.FHB 3/9 x 3/8 x 2/7 = 18504
5. BHH 3/9 x 3/8 x 2/7 =18/504 20.FHH 3/9 x 3/8 x 3/7 = 27/504
6. BHF 3/9 x 3/8 x 3/7 =27/504 21.FHF 3/9 x 3/8 x 2/7 = 18/504
7. BFB 3/9 x 3/8 x 2/7 = 18/504 22.FBB 3/9 x 3/8 x 3/7 = 27/504
8. BFH 3/9 x 3/8 x 3/7 =27/504 23.FBH 3/9 x 3/8 x 2/7 =18/504
9. BFF 3/9 x 3/8 x 2/7 =18/504 24.FBF 3/9 x 2/8 x 3/7 =18/504
10.HBB 3/9 x 3/8 x 2/7 =18/504 25.FFB 3/9 x 2/8 x 3/7 =18/504
11.HBH 3/9 x 3/8 x 2/7 = 18/504 26.FFH 3/9 x 2/8 x 3/7 =18/504
12.HBF 3/9 x 3/8 x 3/7 =27/504 27.FFF 3/9 x 2/8 x 1/7 = 6/504
13.HHB 3/9 x 2/8 x 3/7 = 18/504
14.HHH 3/9 x 2/8 x 1/7 = 6/504
15.HHF 3/9 x 2/8 x 3/7 = 18/504
6+18+18+18+18+27+18+27+18+18+18+27+18+6+18+27+18+18+18+27+18+27+18+18+18+1
8+6 = 504 total
Problem # 2

For example if I had 3 red heart, 3 pink heart and 3 yellow heart. Given three
drawings what are the possible outcomes and the probability percent of each
drawing.

3 red heart 3 pink heart

3 yellow heart
Three Diagram

With Replacement

3/9
3/9
3/9
3/9
3/9
3/9 3/9
3/9
3/9
3/9
3/9
3/9

3/9
3/9
3/9
3/9
3 red heart
3/9 3/9
3 yellow heart
3/9 3/9
3 pink heart
3/9

3/9
3/9
3/9
3/9
3/9
3/9 3/9
3/9
3/9
3/9
3/9 3/9 3/9
3/9
3/9
3/9
3/9
Outcomes

RRR 3/9 x 3/9 x3/9 = 27/ 729 RRY 3/9 x 3/9 x 3/9 =27/ 729
RRP 3/9 x 3/9 x 3/9 = 27/ 729 PPP 3/9 x 3/9 x 3/9 = 27/ 729
RYR 3/9 x 3/9 x 3/9 =27/ 729 It equals 729/729
RYY 3/9 x 3/9 x 3/9 =27/ 729
RYP 3/9 x 3/9 x 3/9 =27/ 729
RPR 3/9 x3/9 x 3/9 =27/ 729
RPY 3/9 x 3/9 x 3/9 =27/ 729
RPP 3/9 x 3/9 x 3/9 = 27/ 729
YRR 3/9 x 3/9 x 3/9 = 27/ 729
YRY 3/9 x 3/9 x 3/9 = 27/ 729
YRP 3/9 x 3/9 x 3/9 =27/ 729
YYR 3/9 x 3/9 x 3/9 =27/ 729
YYY 3/9 x 3/9 x 3/9 =27/ 729
YYP 3/9 x 3/9 x 3/9 =27/ 729
YPR 3/9 x 3/9 x 3/9 =27/ 729
YPY 3/9 x 3/9 x 3/9 =27/ 729
YPR 3/9 x 3/9 x 3/9 =27/ 729
YPY 3/9 x 3/9 x 3/9 =27/ 729
YPP 3/9 x 3/9 x 3/9 =27/ 729
PRR 3/9 x 3/9 x 3/9 =27/ 729
PRY 3/9 x 3/9 x 3/9 =27/ 729
PRP 3/9 x 3/9 x 3/9 =27/ 729
PYR 3/9 x 3/9 x 3/9 =27/ 729
PYY 3/9 x 3/9 x 3/9 =27/ 729
PYP 3/9 x 3/9 x 3/9 =27/ 729
PPR 3/9 x 3/9 x 3/9 =27/ 729
PPY 3/9 x 3/9 x 3/9 = 27/ 729

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