The letters in the word probability are written on separate slips of paper.
Find the probability of drawing two i's in a row without replacement.
prob(2 i's, no replacement)
= (2/11)(1/10) = 1/55
To find the probability of drawing two i's in a row without replacement, we first need to determine the total number of possible outcomes and the number of favorable outcomes.
Step 1: Determine the total number of possible outcomes.
The word "probability" contains 11 letters. Therefore, there are 11 slips of paper with individual letters. When we draw a letter without replacement, the total number of possible outcomes decreases by 1 each time. Hence, the total number of possible outcomes for the first draw is 11, and for the second draw, it is 10.
Step 2: Determine the number of favorable outcomes.
To draw two i's in a row, we must first draw an i on the first draw and then an i on the second draw. Since there are two i's in the word probability, the number of favorable outcomes for the first draw is 2. After the first draw, there is only one i left. Therefore, the number of favorable outcomes for the second draw is 1.
Step 3: Calculate the probability.
Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Thus, the probability of drawing two i's in a row without replacement is:
(2 favorable outcomes) / (11 possible outcomes for the first draw) * (1 favorable outcome) / (10 possible outcomes for the second draw)
Simplifying this expression, we get:
(2/11) * (1/10) = 2/110 = 1/55
Therefore, the probability of drawing two i's in a row without replacement is 1/55.