Question

The letters of the word "INDEPENDENT" are written on individual cards and the cards are
put into a box. A card is selected and then replaced and then a second card is selected.
What is the probability of obtaining the letter "E" twice?

Answer 1

Total cards with letters: 11

Cards with the letter "E": 3

Probability of getting a card with the letter "E": 3/11

If the first card was removed to the side, the second was taken out, and then only the first was removed, then the probability of getting the letter "E" again with the second card: 2/10

Then 3*2/(10*11)=6/110

But if the first card, after being taken out, was put back, and then the card was again chosen at random, then the probability of getting the letter "E"  by the second card: 3/11 again

Then 3/11*3/11 = 9/121