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