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

Answer:

$\frac{25}{144}$

Explanation:

Step1: Calculate first - draw probability

The probability of choosing a vowel on the first draw is $\frac{5}{12}$ since there are 5 vowels out of 12 letters.

Step2: Calculate second - draw probability

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

Step3: Calculate joint probability

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