Geometry

Question Analysis
This question involves calculating the probability of three successive dependent events.
The main focus is on correctly determining the number of favorable outcomes for each event as the sample space changes with each draw and accurately applying the multiplication rule for multiple dependent events.

Key Concept Explanation
For multiple dependent events, the outcome of each previous draw influences the probabilities of the subsequent draws.
As each 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 3 vowels (A, E, I) out of 12 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 11 cards left. The number of consonants is . So .
Calculate the probability of drawing a vowel - labeled card on the third draw given that a vowel - labeled card was drawn first and a consonant - labeled card was drawn second:
After removing two cards, there are 10 cards left, and 2 vowels are left. So

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