Consider the 11 letters of the word MISSISSIPPI. Two of these letters are selected at random, one by one without replacement. What is the probability that

Question

1.) BOTH LETTERS ARE I

2.) NIETHER OF THE LETTERS ARE I

3.) EXACTLY ONE OF THE LETTERS IS P

Answer 1

The first 2 questions are strictly multiplicative:

1) 4/11 chance of an i on the first pick x 3/10 of picking an i on the second pick = 12/110

2) Do it the same way.

3) You can not pick a P, then pick a P or you could reverse the sequence. So the answer will be

2 x (chance of picking a P 1st draw)(chance of not picking a P 2nd draw)