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

3= IIII

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

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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

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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

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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.

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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

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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

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