Answer:

>>> Mathematics

> 16.98

Explain:

To solve this problem, we need to calculate the expected frequency of getting two vowels and one consonant in each draw of three letters. Then, we can use the binomial distribution to calculate the expected frequency for 63 draws. There are 3 vowels and 5 consonants in the word KALIMETO. Therefore, the probability of getting 2 vowels and 1 consonant is:

> P(2 vowels and 1 consonant) = P(first vowel) × P(second vowel) × P(consonant) + P(first vowel) × P(consonant) × P(second vowel) + P(consonant) × P(first vowel) × P(second vowel)

> Where P(vowel) = 3/8 and P(consonant) = 5/8.

> So, P(2 vowels and 1 consonant) = (3/8) × (2/7) × (5/6) + (3/8) × (5/6) × (2/7) + (5/8) × (3/8) × (2/7) = 15/56

Therefore, the expected frequency of getting two vowels and one consonant in each draw of three letters is 15/56. To calculate the expected frequency for 63 draws, we can use the binomial distribution with n = 63 and p = 15/56:

> E(X) = np = 63 × 15/56 ≈ 16.9

→ So, the expected frequency of getting two vowels and one consonant in 63 draws of three letters is approximately 16.98 ✓

• 6 March 2023