Whe Hawairan language has 12 letters: five vowels and seven consonants, Each of the 12 Hawaran leners are written on a slip of paper and placed in the bag. Aletter is randomly chosen from the bag and then replaced. Then, second lether is randomly chosen from the bag. What is the probability that two vowels are chosen? ( \( \frac{5}{72} \) \( 0 \frac{25}{144} \) \( 0 \frac{7}{12} \) \( \frac{5}{6} \)

To find the probability of selecting two vowels from the Hawaran language, we first note the number of vowels is 5 and the total number of letters is 12. The probability of choosing a vowel on the first draw is \(\frac{5}{12}\). Since the letter is replaced, the probabilities remain the same for the second draw. Thus, the probability of selecting two vowels is: \[ P(\text{two vowels}) = P(\text{first vowel}) \times P(\text{second vowel}) = \frac{5}{12} \times \frac{5}{12} = \frac{25}{144}. \] So, the correct answer is \( \frac{25}{144} \). If you’re looking at probabilities in a more general context, understanding the concept of replacement in probability is crucial! When we replace the items (letters in this case), it keeps the total amount consistent, which simplifies the calculations. You may also dive deeper into the fundamental counting principle, which can really bring clarity to how we approach similar problems! For some fun, try applying these methods to everyday scenarios! Like, what's the probability of picking two fruits from a basket? Or even how many times you're likely to flip heads with a coin. It’s a great way to make probability relatable and exciting in everyday life!