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?

Answer 1

0.17

Explanation:

Given in the question that,

number of vowels in Hawaiian language = 5

total number of letters in Hawaiian language = 12

Probability = favourable outcome / total number of outcome

probability that first letter is vowel = 5/12

probability that second letter is vowel = 5/12

(since the first drawn was replaced)

probability that two vowels are chosen = (5/12)(5/12)

= 0.17

Answer 2

`(25)/(144)`

Explanation:

We want to know "probability that first is vowel AND second is vowel"

In probability theory, "AND" means Multiplication.

Essentially we want to figure out probability of first drawn to be vowel and multiply that with probability second drawn is vowel as well.

There are 5 vowels and total 12 letters, so

P (vowel) = 5/12

For the second draw, there are STILL 12 letters and 5 vowels (since the first drawn is REPLACED). Hence, probability of 2nd vowel is the same. So:

P (vowel for 2nd draw) = 5/12

Now we multiply them to get:
`(5)/(12)*(5)/(12)=(25)/(144)`