Probability Tree Diagrams

There are 6 red balls out of a total of 10 balls. The probability of drawing a red ball is $\frac{6}{10}$, which simplifies to $\frac{3}{5}$.

There are 4 blue balls out of 10 total balls. The probability is $\frac{4}{10}$, which simplifies to $\frac{2}{5}$.

After drawing one blue ball, there are 3 blue balls left out of 9 total balls. The probability is $\frac{3}{9}$, which simplifies to $\frac{1}{3}$.

After drawing one blue ball, there are 6 red balls left out of 9 total balls. The probability of drawing a red ball is $\frac{6}{9}$, which simplifies to $\frac{2}{3}$.

The probability of drawing a red ball first is $\frac{6}{10}$. The probability of drawing a blue ball second is $\frac{4}{9}$. Multiplying gives $\frac{24}{90}$, which simplifies to $\frac{4}{15}$.

There are two possible outcomes: drawing red then blue, or blue then red. Red then blue has probability $\frac{6}{10}\times \frac{4}{9}=\frac{24}{90}$. Blue then red has probability $\frac{4}{10}\times \frac{6}{9}=\frac{24}{90}$. Adding gives $\frac{48}{90}$, which simplifies to $\frac{8}{15}$.