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?
\( \frac{10}{15} \cdot \frac{10}{15} \)
\( \frac{10}{15} \cdot \frac{9}{15} \)
\( \frac{10}{15} \cdot \frac{9}{14} \)
\( \frac{5}{15} \cdot \frac{4}{14} \)

Answer

Expert–verified

Hide Steps

Answer

\( P(\text{not yellow}) = 1 - \frac{5}{15} \cdot \frac{4}{14} = \frac{10}{15} \cdot \frac{9}{14} \)

Steps

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 ：\( P(\text{not yellow}) = 1 - \frac{5}{15} \cdot \frac{4}{14} = \frac{10}{15} \cdot \frac{9}{14} \)