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 one vowel

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

Step2: Find probability of two vowels

Since the first letter is replaced, the two draws are independent events. The probability of two independent events both occurring is the product of their individual probabilities. So the probability of choosing two vowels is $\frac{5}{12} \times \frac{5}{12} = \frac{25}{144}$.

Answer:

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