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)?
A. one fifth
B. two fifths
C. three fifths
D. two over twenty-five
The word Paris has five letters: P, A, R, I, and S. Since each letter is replaced after it is drawn, the probability of getting P on the first draw is 1/5 (there is one P out of five letters).
Now, there are four letters left in the bag, including two vowels (A and I) and two consonants (R and S). Therefore, the probability of drawing a vowel on the second draw, given that P was drawn first, is 2/4 or 1/2 (there are two vowels out of four letters).
To find the probability of both events happening (P first, then vowel), we multiply their probabilities:
P(P, then vowel) = P(P) x P(vowel after P)
P(P, then vowel) = 1/5 x 1/2
P(P, then vowel) = 1/10
Therefore, the answer is A. One fifth.
To find the probability of drawing a 'P' first and then a vowel, we need to determine the number of 'P' and vowel combinations divided by the total number of possible combinations.
Let's start by finding the probability of drawing a 'P' first. Since there is only one 'P' in the word Paris, the probability of selecting 'P' first is 1 out of 5.
Next, we need to find the probability of drawing a vowel after selecting 'P'. In the word Paris, there are two vowels, 'a' and 'i', remaining after selecting 'P'. So, the probability of drawing a vowel after selecting 'P' is 2 out of 5.
To find the probability of both events occurring, we multiply the probabilities together. Therefore, the probability of drawing a 'P' first and then a vowel is (1/5) * (2/5) = 2/25.
So, the answer is D. two over twenty-five.