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

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