The letters of the word Mississippi are placed in a hat. What is the probability that the first two letters drawn are both i if the first letter drawn is not replaced?

Correct

four i's, 11 letters total

prob of given case = (4/11)(3/10) = 12/110 = 6/55

or

C4,2)/C(11,2) = 6/55

To find the probability of drawing two "i"s consecutively from the word "Mississippi" without replacement, we need to calculate the number of favorable outcomes and the total number of possible outcomes.

Step 1: Count the favorable outcomes:
The word "Mississippi" has a total of 11 letters. There are 4 "i"s in the word, and we want to draw two of them consecutively without replacement.

The first "i" can be drawn in one of the 4 available spots. Once the first "i" is drawn, there will only be 3 remaining "i"s left. So, the second "i" can be drawn in one of the 3 available spots.

The total number of favorable outcomes is, therefore, 4 * 3 = 12.

Step 2: Count the total number of possible outcomes:
The word "Mississippi" has a total of 11 letters, and we are drawing 2 letters without replacement.

The first letter can be any of the 11 letters in the word. Once the first letter is drawn, there are 10 remaining letters in the word. So, the second letter can be any of the remaining 10 letters.

The total number of possible outcomes is, therefore, 11 * 10 = 110.

Step 3: Calculate the probability:
The probability is given by the ratio of favorable outcomes to total outcomes.

Probability = Favorable outcomes / Total outcomes
Probability = 12 / 110

Reducing the fraction:
Probability = 6 / 55

Therefore, the probability that the first two letters drawn are both "i"s, without replacement, is 6/55.

To determine the probability of drawing two "i"s from the word "Mississippi" without replacement, we need to count the total number of possible outcomes and the number of favorable outcomes.

First, let's calculate the total number of possible outcomes. The word "Mississippi" has 11 letters in total. So when you draw the first letter, you have 11 options.

Next, we need to determine the number of favorable outcomes, i.e., the number of ways to draw two "i"s. There are 4 "i"s in the word "Mississippi". For the first draw, you have 4 "i"s to choose from. After you draw the first "i", there are only 3 "i"s left out of the remaining 10 letters in the hat.

Therefore, the number of favorable outcomes is 4 * 3 = 12.

The probability of drawing two "i"s without replacement can be calculated as the number of favorable outcomes divided by the total number of possible outcomes.

Probability = Number of favorable outcomes / Total number of possible outcomes
= 12 / 11

Simplifying, we have:
Probability = 1.09 (rounded to two decimal places)

So, the probability of drawing two "i"s without replacement is approximately 1.09 or 109%.