Experimental Probability

So we’re going to base our experimental probability on this video HERE

So we have a spinner:


The way I’m doing this problem is I am taking a spinner like this at home and I’m spinning it 10 times. I am putting a tally next to the number to see how many times I got the result.

1= III

2= I


4= II

So I will write the probabilities with the denominator as 10 and the numerator as what the result of the number is.

1 = 3/10

2= 1/10

3= 4/10 = 2/5

4= 2/10 = 1/5

So the probability of getting a 4 is 1/5.

If I wanted to know the probability of getting anything under a 3 would be

3/10 + 1/10 = 4/10 = 2/5


Probability with letters

So throughout my blog i have shown you examples of different probabilities. I think it’s important to see the difference between if you take a letter out of a bag and replace it or if you don’t replace it. Here’s an example:

You have the word HIPPO. What are the odds you will draw out the word HIP from Hippo with replacement?

So there are 6 letters and each one will be made into a fraction. The denominator the total number of letters and the numerator is the number of letters in the word.

H=1/6 I=1/6 P=2/6

So we will multiply these letters from the bag to spell HIP

1            1      2       2        1

—  X  — X — =  —  =  —   so the probability of drawing HIP is 1 out of 108

6            6      6     216    108

Now lets do it without replacement:

Every time you take on out, the denominator will drop one number since it is not being put back.

H=1/6 I=1/5 P=2/4

So now you multiply them

1        1           2       2          1

—  X  — X — =  —   =   — So the odds of spelling out Hippo is 1 out of 60

6        5           4      120      60

You can do this with a lot of different letters and situations. This was just an easy example to show how you can do it mathematically.

This is another example of probability with replacement. here

Tree Diagram and Probabilities

So there are tons of ways to conduct probability problems. One such way is through a Tree Diagram. This is great for children who don’t do well just thinking it out and need a visual representation. So here’s a problem using a dilemma many people have, such as how many boys or girls they would have probability wise.

So here’s a problem. A woman wants to know the odds of her having all girls if she has 3 children so we are going to make a tree diagram.


What is the probability that they will only have boys?

So first off the outcome of a boy or a girl is always 1/2. So the combinations are as follows:

MMM = 1/2 X 1/2 X 1/2 = 1/8, MMF = 1/2 X 1/2 X 1/2 = 1/8, MFF = 1/2 X 1/2 X 1/2 = 1/8

MFM = 1/2 X 1/2 X 1/2 = 1/8 FFF = 1/2 X 1/2 X 1/2 = 1/8 = 1/2, FMF = 1/2 X 1/2 X 1/2 = 1/8

FMM = 1/2 X 1/2 X 1/2 = 1/8

So the probability of getting at least 2 males is:

1/8 + 1/8 + 1/8 + 1/8 = 4/8 = 1/2

So this is a basic way of showing probability. Theres lots of different outcomes. Another example is the probability of getting all males is 1/8 since there are 8 outcomes.

The best part is no matter what this is an example of a theoretical probability. If you would like to see more examples of tree diagrams click here

Odds of rolling a dice

So last time we went over probability and figured out the mathematical equations associated with them. Now we’re going to discuss what are odds?

Odds are: describing the likelihood of an event but it is discussing the number of successes vs the number of failures.

So today We will be discussing an item that everyone has had an encounter with, DICE! We will be using a die to figure out the odds of having a successful outcome. So the formula we are going to use is:

if it’s in favor:

Number of ways that an event could occur


Number of ways that the event could not occur

so in the case of our dice we know there are 6 sides (1,2,3,4,5,6)


So the problem we are going to work on is what are the odds of rolling a number less than 3?

in favor  (1,2,)                 2              1

———————–   =   ——  =  ———–   so the odds of rolling a # less than 3 is 2:1

not favor (3,4,5,6)           4              2

Lets also do the odds against an event:

Number of ways that event could not occur


Number of ways that event could occur

So if we use the problem above, it’s just the inverse. So:

not favor (3,4,5,6)                 4                   2

————————   =   ——–  =  ——- so the odds against it are 2:1

in favor (1,2)                          2                   1

If you would like to see more probability answers, feel free to click here.

Cards and probability

I wanted to start my project on Probability by relating it to a common object we use pretty often and have a great knowledge of. Plus if you want to gamble later in life, probability is your friend ;).

So today we will be talking about cards and probabilities. First off to start a probability problem you need to know how to set it up. Here’s the formula we use to figure this out:

Probability is: the likelihood that a particular event will occur.

Probability of a possible outcome


Total number of items

So if we are using a deck of cards, we can figure out through knowledge that there are 52 cards, if not you can lay out the suits like I did in the is picture to figure it out.


there are 13 suits and 4 in each suit so therefore 4X13 =52

So the first problem we are going to do is finding the probability of getting a red card out of the deck of cards:

By looking at the picture below you can see each suit has 2 red cards. therefore if there are 13 suits that would be 13X2= 36. because there are 2 in each of the suits:


so the problem would be as follows:

Number of red cards                     26                               1                 I reduced the fraction

————————–         =   ————–   =             ————          because you always

total number of cards                    52                               2                reduce them by division

There are plenty more problems you can do with cards as well. Another example is:

How many face cards will you get out of a deck of cards?

There are 3 face cards (Jack, Queen, King) and each one has 4 suits (spades, clubs, hearts and diamonds) so therefore the problem would be 3X4 =12

So the problem would be 12/52 and when you reduce it, it would be 2/13.

Next time you go out to play cards. Remember some of these tips to help figure out the probability of getting what your looking for. 😀

Here’s an example of using probability and playing cards to make a venn diagram to illustrate the outcomes as well HERE

Welcome to one of my biggest fears…

So when many people here the word math, they get very nervous. The numbers fly through their head, their imagination runs wild. Not to mention word problems…those scare me the most it’s as if the walls are closing in on me and I want to scream! D:


Though in reality…Math is really all about picking the simple pieces out of information and breaking it down. Word problems used to scare me the most but now they seem a lot more easier the more I take my time, *breathe* and slowly read it out. Now that I have gone on about my history with math, let me tell you what we’re going to be breaking down and how it relates to our actual life.

WELCOME TO PROBABILITY!! First thing everyone asks:

When will I ever use this?

Well oddly enough figuring out the odds in everyday life happens constantly. Whether it’s the probability its going to rain or whether you are going to win rock paper scissors against someone on who is going to take out the trash. It’s all around us. So don’t be scared. I’m going to break this down really easy. We’ll start in my next post about cards.

To help introduce probabilities and have a calculator help you illustrate demonstrations click HERE