Question

the hawaiian language has 12 letters: five vowels and seven consonants. each of the 12 hawaiian letters are written on a slip of paper and placed in the bag. a letter is randomly chosen from the bag and then replaced. then, a second letter is randomly chosen from the bag. what is the probability that two vowels are chosen? \\(\frac{5}{72}\\) \\(\frac{25}{144}\\) \\(\frac{7}{12}\\) \\(\frac{5}{6}\\)

Explanation:

Step1: Find probability of first vowel

There are 5 vowels out of 12 letters. So the probability of choosing a vowel first is $\frac{5}{12}$.

Step2: Find probability of second vowel (with replacement)

Since we replace the first letter, the situation is the same. So the probability of choosing a vowel second is also $\frac{5}{12}$.

Step3: Multiply the two probabilities

To find the probability of both events happening (choosing a vowel first and then a vowel second), we multiply the two probabilities: $\frac{5}{12} \times \frac{5}{12} = \frac{25}{144}$.

Answer:

$\frac{25}{144}$ (corresponding to the option $\boldsymbol{\frac{25}{144}}$)