To determine the probability of picking a consonant first and then a vowel, we first identify the letters on the cards. The letters we have are A, M, O, L, and S.
Step 1: Identify consonants and vowels.
- Vowels: A, O
- Consonants: M, L, S
Step 2: Count the letters.
- Total number of letters: 5
- Number of vowels: 2 (A, O)
- Number of consonants: 3 (M, L, S)
Step 3: Calculate the probabilities.
-
Probability of picking a consonant first: \[ P(\text{Consonant}) = \frac{\text{Number of consonants}}{\text{Total number of letters}} = \frac{3}{5} \]
-
Probability of picking a vowel second (after replacing the first card): \[ P(\text{Vowel}) = \frac{\text{Number of vowels}}{\text{Total number of letters}} = \frac{2}{5} \]
Step 4: Calculate the combined probability. Using the multiplication rule for independent events (since the card is replaced): \[ P(\text{Consonant first and Vowel second}) = P(\text{Consonant}) \times P(\text{Vowel}) = \frac{3}{5} \times \frac{2}{5} = \frac{6}{25} \]
Thus, the probability that the first card is a consonant and the second card is a vowel is \(\frac{6}{25}\).
Final answer: \(\frac{6}{25}\)