The letters in the word Paris are written on slips of paper and placed in a bag. Each letter will be put back after it is drawn. What is P(r, then vowel)?
done before
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To find the probability of drawing a specific sequence of letters from the bag, we need to know the total number of possible outcomes and the number of favorable outcomes.
First, let's determine the total number of possible outcomes. Since each letter is put back into the bag after it is drawn, there are a total of 5 letters in the word "Paris", and each letter has a chance to be drawn at each stage. Therefore, there are 5 choices for the first letter, 5 choices for the second letter, and so on, resulting in a total of 5 × 5 × 5 × 5 × 5 = 5^5 = 3125 possible outcomes.
Next, we need to determine the number of favorable outcomes, which in this case is the number of ways to get the sequence "P(r, then vowel)". To calculate this, we split it into two steps:
Step 1: First letter is 'P'. In this case, we have 1 favorable outcome.
Step 2: The second letter is 'r', and the third letter is a vowel. There are 2 vowels in the word "Paris": 'a' and 'i'. Therefore, we have 1 favorable outcome for the second letter ('r') and 2 favorable outcomes for the third letter (each vowel). This gives us a total of 1 × 1 × 2 = 2 favorable outcomes.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability of P(r, then vowel) = Number of favorable outcomes / Number of possible outcomes
= 2 / 3125
= 2/3125
Thus, the probability of drawing the sequence "P(r, then vowel)" from the bag is 2/3125.