A bag has 3 red and 5 blue balls. Two are drawn without replacement. What is the probability both are red?

Problem: Find the probability of drawing two red balls without replacement from a bag containing $3$ red and $5$ blue balls.

Steps

1. Find the total number of balls
   $$3 + 5 = 8$$
2. Find the probability of drawing a red ball on the first draw
   $$\frac{3}{8}$$
3. Find the probability of drawing a red ball on the second draw given the first was red
   $$\frac{2}{7}$$
4. Multiply the probabilities of both dependent events
   $$\frac{3}{8} \times \frac{2}{7} = \frac{6}{56}$$
5. Simplify the fraction
   $$\frac{3}{28}$$