Final answer:
The probability that the first letter is A in the word ARIZONA is 1/7, and the probability of the first letter being Z is 0. The probability that the first letter is a vowel is 3/7, and the probability of the first letter being H is 0.
Step-by-step explanation:
To find the probability of an event occurring, we divide the number of favorable outcomes by the total number of possible outcomes. In the case of the word ARIZONA, there is only one A out of a total of 7 letters. Therefore, the probability that the first letter is A is 1/7.
Since there is no Z in the word ARIZONA, the probability of the first letter being Z is 0.
There are 3 vowels (A, I, O) out of 7 letters in the word ARIZONA. Therefore, the probability that the first letter is a vowel is 3/7.
Again, since there is no H in the word ARIZONA, the probability of the first letter being H is 0.