A deck of cards contains 12 cards with letters and 16 cards with numbers. A card is pulled from the at random and replaced. This process is carried out 14 times. What is a reasonable prediction for the numbeli of times a card with a letter should be chosen? *Must show work*

To solve this problem, we need to determine the probability of drawing a card with a letter and then use that probability to predict how many times a letter card will be drawn in 14 attempts. ### Step 1: Determine the total number of cards The total number of cards in the deck is the sum of the letter cards and the number cards: \[ \text{Total cards} = \text{Number of letter cards} + \text{Number of number cards} = 12 + 16 = 28 \] ### Step 2: Calculate the probability of drawing a letter card The probability \( P(L) \) of drawing a letter card is given by the ratio of the number of letter cards to the total number of cards: \[ P(L) = \frac{\text{Number of letter cards}}{\text{Total cards}} = \frac{12}{28} \] ### Step 3: Simplify the probability We can simplify \( \frac{12}{28} \): \[ P(L) = \frac{12 \div 4}{28 \div 4} = \frac{3}{7} \] ### Step 4: Predict the number of times a letter card will be drawn To predict the number of times a letter card will be drawn in 14 attempts, we multiply the total number of attempts by the probability of drawing a letter card: \[ \text{Expected number of letter cards} = 14 \times P(L) = 14 \times \frac{3}{7} \] ### Step 5: Calculate the expected number Now we perform the multiplication: \[ \text{Expected number of letter cards} = 14 \times \frac{3}{7} = 14 \div 7 \times 3 = 2 \times 3 = 6 \] ### Conclusion A reasonable prediction for the number of times a card with a letter should be chosen in 14 attempts is \( \boxed{6} \).