Problem
A deck of flash cards has 4 blue, 5 yellow, and 6 red cards. Two cards are selected from the deck without replacement. Which expression correctly gives the probability that both cards are not yellow? \( \frac{10}{15} \cdot \frac{10}{15} \) \( \frac{10}{15} \cdot \frac{9}{15} \) \( \frac{10}{15} \cdot \frac{9}{14} \) \( \frac{5}{15} \cdot \frac{4}{14} \)
Solution
Step 1 ：\( P(\text{not yellow}) = 1 - P(\text{both yellow}) \)
Step 2 ：\( P(\text{both yellow}) = \frac{5}{15} \cdot \frac{4}{14} \)
Step 3 ：\( P(\text{not yellow}) = 1 - \frac{5}{15} \cdot \frac{4}{14} = \frac{10}{15} \cdot \frac{9}{14} \)
