Geometry

Question Analysis
This question focuses on calculating the probability of two successive dependent events.
The main emphasis is on correctly determining the number of favorable outcomes for each event as the sample space changes with the first draw, and accurately applying the multiplication rule for dependent events.

Key Concept Explanation
Dependent events imply that the outcome of the first card draw influences the probabilities of the second draw.
As a card is removed, the total number of cards and the number of cards with specific characteristics (vowels or consonants) decrease, altering the probabilities for the next draw.

Step-by-Step Solution
Calculate the probability of drawing a vowel - labeled card on the first draw:
There are 2 vowels (A, E) out of 8 cards, so .
Calculate the probability of drawing a consonant - labeled card on the second draw given that a vowel - labeled card was drawn on the first draw:
After removing one vowel - labeled card, there are 7 cards left. The number of consonants is . So