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: Probability of one vowel

Probability of picking a vowel: $\frac{5}{12}$

Step2: Multiply for two independent picks

Since the letter is replaced, the events are independent. Multiply the probabilities: $\frac{5}{12} \times \frac{5}{12}$

Step3: Calculate the product

$\frac{5 \times 5}{12 \times 12} = \frac{25}{144}$

Answer:

$\frac{25}{144}$ (Option: $\boldsymbol{\frac{25}{144}}$)