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

The probability of drawing two red balls without replacement is 5/8 × 4/7 = 20/56 = 5/14 ≈ 0.357

Step-by-Step Solution:
First draw: P(R₁) = 5/8 (5 red out of 8 total)
Second draw: P(R₂|R₁) = 4/7 (4 red remaining out of 7 total)
Apply multiplication rule for dependent events: P(R₁ and R₂) = P(R₁) × P(R₂|R₁)
Calculate: 5/8 × 4/7 = 20/56 = 5/14

Key Mistake to Avoid: Don't multiply 5/8 × 5/8 - this incorrect approach assumes replacement, which would make events independent.



Quick Tip: In 'without replacement' problems, always adjust the denominator AND numerator for subsequent probabilities - both decrease by 1.