Question

What is the probability of picking a card with a vowel on it, replacing it, and then picking another vowel from cards with the following letters: B, A, N, A, N, A?

a) 1/3
b) 1/2
c) 2/3
d) 1

Answer 1

The probability of picking a card with a vowel on it, replacing it, and then picking another vowel from the given cards is 1/4.

Step-by-step explanation:

To find the probability of picking a card with a vowel on it, replacing it, and then picking another vowel from the given cards, we first need to determine the total number of cards that have vowels on them. From the given letters B, A, N, A, N, A, there are three vowels (A) and three consonants (B, N, N).

Since we are replacing the card after each draw, the probability of picking a vowel on the first draw is 3/6 (since there are 3 vowels out of 6 total cards). The probability of picking another vowel on the second draw is also 3/6. To find the overall probability, we multiply the individual probabilities:

Probability of picking a vowel on the first draw = 3/6

Probability of picking a vowel on the second draw = 3/6

Overall probability = (3/6) * (3/6) = 9/36 = 1/4

Therefore, the probability of picking a card with a vowel on it, replacing it, and then picking another vowel from the given cards is 1/4.