Question

Brandi has a deck of 12 cards labeled A through L. Brandi draws a card from the deck and returns it, then draws a card again. What is the theoretical probability that Brandi draws a card with a vowel both times?

A) 6.25%

B) 2.08%

C) 25%

D) 75%

Answer 1

A) 6.25%

Explanation:

There are 3 vowels (A, E, I ) in the deck of 12 cards A thru L

The probability of drawing a vowel on the first draw is 3/12. Since the card is returned, the deck still has 12 cards, including 3 vowels and 9 consonants.

The probability of drawing a vowel on the second draw, given that a vowel was drawn on the first draw, is 3/12.

To find the probability of both events occurring, we multiply the probabilities:

P(vowel on first draw) x P(vowel on second draw given that a vowel was drawn on the first draw) = (3/12) x (3/12) = 9/144 = 1/16 = .0625 = 6.25%

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