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