Question

A bag contains 5 red, 3 blue, and 2 green balls. If two balls are drawn at random without replacement, what is the probability that both are red?

• A. \( \frac{1}{2} \)
• B. \( \frac{1}{3} \)
• C. \( \frac{5}{9} \)
• D. \( \frac{1}{6} \)

Hint:

Use combinations to calculate probabilities when dealing with random draws without replacement.

Answer 1

The Correct Option is D

The total count of balls is \( 5 + 3 + 2 = 10 \). The combinations for selecting 2 balls from 10 are \( \binom{10}{2} = 45 \). The combinations for selecting 2 red balls from the 5 available red balls are \( \binom{5}{2} = 10 \). Therefore, the probability of selecting two red balls is \( \frac{10}{45} = \frac{1}{6} \). The confirmed result is \( \boxed{\frac{1}{6}} \).