How To Construct, Make, Draw A Tree Diagram And What Is A Tree Diagram In For Probability Math

In this video we discuss how to construct or draw a tree diagram for probability and statistics. We give examples and also go through how to use a tree diagram to calculate probabilities.
Transcript/notes
A tree diagram is basically a visual way to write out a sample space and calculate probabilities. For instance we could draw a tree diagram for flipping a coin a coin 3 times.
So, the first flip could be heads or tails, so we branch these off from one another. And at the end of these branches we can put an H or a T for heads or tails.
Now we can address the second flip, which again can only be a head or a tail, 2 possibilities. So, from both the H and the T, we can put in 2 branches to represent the possibilities.
If the first flip resulted in a head, the second flip could be a head or a tail, so at the end of the branches from the first flip being a head, we again put an H or a T. And we can do the same for the bottom portion of the diagram, if the first flip was a tail, second flip could be a head or a tail, so an H and a T at the end of the branches from first flip being a tail.
So, now after 2 flips, we have 4 different possible paths so to speak, and for the third flip, there again are only 2 possibilities, heads or tails. So from each of these, we can draw in 2 branches outwards. And at the end of the branches on the top path, head on flip one, and head on flip 2, we can address flip number 3. There can only be a head or a tail for flip 3, so we write in an H and a T at the end of these branches.
And we can write these possibilities in for the end of the branches for the other 3 paths, H or T. So, after doing all of this we have a total of 8 possible paths, or outcomes. And we can write those in on the right side of the diagram to make it a bit clearer.
So, at the end of path 1, we would have gotten a head on flip 1, a head on flip 2 and a head on flip 3, so HHH for the outcome. Next we have head on flip 1, head on flip 2, and a tail on flip 3, so HHT. And you would go through the rest of the paths or branches and fill in the possible outcomes as you see on the screen.
Tree diagrams also make it somewhat easy to calculate probabilities. Starting with coin flip number one, we can get a head or a tail, so there is a 50% probability of either, which is 0.5, or fractionally 1 over 2. So, we can write that in near the branch going to H for coin flip number one, and do the same for the branch going to T for coin flip number one.
And we can actually write in 0.5 for each branch in the diagram, because there is always a 50% probability of being a head or a tail.
Now we can calculate the probabilities for the outcomes. So, lets look at flip one being a tail, flip 2 being a head and flip 3 being a tail. If we go though our branches, we have 0.5 probability flip one is a tail, then a 0.5 probability flip 2 is a head, and a 0.5 probability that flip 3 is a tail.
To calculate the probability of tail, head, tail, we multiply the probabilities, so, 0.5 times 0.5 times 0.5, which equals 0.125 or 12.5%. We could do this fractionally as well, 1 over 2 times 1 over 2 times 1 over 2 equals 1 over 8 which equals 0.125.
Drawing a picture in many cases makes things clearer, and here is an example of a tree diagram kind of showing this.
Let’s say you want to know the probability that your favorite hockey team is going to win its next 2 games. You do some statistical wizardry and come up with your own probabilities for their next 2 games.
I have a tree diagram for the 2 games and the possible outcomes. For game 1 they could win, lose or tie. Your calculations give them a probability of 58% to win, 26% to lose and 16% of tying. Regardless of the results of game 1, your calculations for game 2 give them a 72% probability to win, 24% probability of losing and a 4% probability of tying.
To keep this video short, I have written in all the probabilities on all of the branches. Going down the branch of win game 1, and win game 2, we have 0.58 times 0.72, which equals 0.418, or a 41.8% probability to win the back to back games.
On the right I have listed the 9 possible outcomes, and by totaling all of the probabilities, we see the lowest probability is a tie and a tie at less than 1%. And the highest probability is actually to win game one and win game two.
But you can see that this gives you a nice visual to look at and understand, rather than just numbers, which can often times make it easy to get lost and confused.
Timestamps
0:00 What Is A Tree Diagram?
0:08 Coin Flip Example
1:20 Coin Flip Possible Outcomes
1:49 Calculate Probabilities Using A Tree Diagram
2:58 Probability Example Problem

[@waterproofwater9444]

Thank you so much. This video helped a lot. Just learned 3 math lessons in one video 👍👍👍

[@whatsupdude2778]

Awesome to hear the video helped you out, thanks for sharing that Donnelle Jana Thayalan.

[@Deathsong19]

Thanks you so much, you explained this better then my math book did

[@tilenjan42]

wow such an interesting video. learnt so much from it. Thank you from Solvenia xxxx

[@fizzy_train6286]

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[@AhmedBabikir6969]

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[@whatsupdude2778]

Awesome, great to hear the video helped you out, and thanks for the support.

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people who are here one day before the exam cramming everything like me
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This was a great video jus next time maybe not use a black background because it was a bit hard to focus on the video. But other then that great job!!!

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[@AbAb-mm3og]

'liked'. Thank you for the video. If I am the observer of the three coin tosses, then the probability of a H or T showing up are 12.5%. but if someone else came in after the first toss was over, then for that person, the probability of an H or T is 25%? (1/2 * 1/2 = 1/4). So this seems like relativity - things will appear different based on where you are standing (similar to real life). Perhaps I am reading too much into it.

[@whatsupdude2778]

Hey Ab Ab, you are correct, for 2 coin tosses the possible outcomes decreases, so the probability of each of those outcomes increases (3 tosses = 12.5% for each outcome, 2 tosses = 25% for each outcome). Probability can be confusing at times, the main thing is to have a basic understanding of it.

[@AbAb-mm3og]

@@whatsupdude2778 Thank you.

[@rubathdewan2723]

how can i know if the player's winning probability is 0.58 and loosing probability is 0.26 and probability of being tie is 0.16 at first??can u tell me please??

[@Eli-ux8bn]

This was posted on my birthday

[@aminhadi6679]

wht i didnt understand is tht, the sample space is 9 and the even of winning 2 games in a raw is 1 so the probability should be 1/9= 11.11%...so why did he say tht the probability is 41.8%

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So u where born on feb 16
Edit:scroll to the bottom to know what I’m talking about