the hawaiian language has 12 letters, five vowels and seven consonants. each of the 12 hawaiian letters are…

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?\n\\(\\frac{5}{72}\\)\n\\(\\frac{25}{144}\\)\n\\(\\frac{7}{12}\\)\n\\(\\frac{5}{6}\\)

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?\n\\(\\frac{5}{72}\\)\n\\(\\frac{25}{144}\\)\n\\(\\frac{7}{12}\\)\n\\(\\frac{5}{6}\\)

Answer

Explanation:

Step1: Calculate probability of first - vowel

The probability of choosing a vowel on the first draw is the number of vowels divided by the total number of letters. There are 5 vowels and 12 total letters, so the probability $P_1=\frac{5}{12}$.

Step2: Calculate probability of second - vowel

Since the letter is replaced, the probability of choosing a vowel on the second draw is also $\frac{5}{12}$ because the situation is the same as the first draw.

Step3: Calculate probability of both events

For independent events, the probability of both events occurring is the product of their individual probabilities. So $P = P_1\times P_2=\frac{5}{12}\times\frac{5}{12}=\frac{25}{144}$.

Answer:

$\frac{25}{144}$