Two letters are selected at random from the word “MISSISSIPPI

Question

Two letters are selected at random from the word “MISSISSIPPI”. ”. What

is the probability that the selection is two “I” s?

Answer 1

Hello, thank you for taking the time to post your question!

When you are computing a probability like this you want to start by thinking about how many total ways that 2 letters could be picked out of the word. So it has 11 letters total, meaning that we want to compute 11, choose 2

C(11,2) = 11! / (2!(11-2)!) = 11! / 2!9! = (11 x 10) / (2 x 1) = 55

Meaning that there are 55 possible ways to select two letters from the word “MISSISSIPPI”

Since the question is asking specifically about the chances of finding the letter “I” then you want to find C(4,2) since there are 4 I’s in the word Mississippi

C(4,2) = 4! / 2!(4-2)! = 4! / 2!2! = (4 x 3) / (2 x 1) = 6

Putting it all together then would make the total probability 6/55

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

There are 11 letters in "Mississippi", four of which are "i"s.  Hence the odds of picking an "i" on the first pick are 4/11.  If you pick an "i", there are 10 letters left, 3 of which are "i"s, so the probability of picking an "i" on that try are 3/10.  The odds of picking two "i"s on consecutive tries are (4/11)*(3/10) = 12/110 = 6/55.