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

Answer 2

To calculate the probability of obtaining the letter "E" twice from the word "INDEPENDENT," we need to consider the total number of cards in the box and the number of cards with the letter "E."

Total Number of Cards:

The word "INDEPENDENT" has a total of 11 letters. Therefore, there are 11 cards in the box.

Number of Cards with the Letter "E":

The word "INDEPENDENT" has two occurrences of the letter "E." Therefore, there are two cards with the letter "E" in the box.

Probability Calculation:

To calculate the probability, we divide the number of favorable outcomes (selecting the letter "E" twice) by the total number of possible outcomes (selecting any two cards from the box).

The probability of selecting the letter "E" on the first draw is 2 out of 11, as there are two cards with the letter "E" out of a total of 11 cards.

After the first card is selected and replaced, the probability of selecting the letter "E" on the second draw remains the same, as the cards are replaced.

To find the probability of both events occurring (selecting the letter "E" twice), we multiply the probabilities of each event together.

Therefore, the probability of obtaining the letter "E" twice from the word "INDEPENDENT" is (2/11) * (2/11) = 4/121.

Please note that this calculation assumes that each card has an equal chance of being selected and that the selection process is random.