Question

A bag contains 10 green balls and 5 red balls. If two balls are selected randomly, then the probability that both are green balls, is:

• A. \( \frac{9}{35} \)
• B. \( \frac{2}{7} \)
• C. \( \frac{3}{7} \)
• D. \( \frac{5}{27} \)
• E. \( \frac{2}{15} \)

Hint:

When calculating the probability of selecting two specific items without replacement, multiply the probabilities of each selection in sequence.

Answer 1

The Correct Option is C

We are given that there are 10 green balls and 5 red balls in the bag, so the total number of balls is:

\[ 10 + 5 = 15 \]

We need to find the probability that both balls selected are green. The probability of selecting the first green ball is:

\[ P(\text{1st green}) = \frac{10}{15} \]

After selecting the first green ball, there are 9 green balls left and 14 balls in total, so the probability of selecting the second green ball is:

\[ P(\text{2nd green}) = \frac{9}{14} \]

The total probability of selecting two green balls is the product of the probabilities:

\[ P(\text{both green}) = \frac{10}{15} \times \frac{9}{14} = \frac{90}{210} = \frac{3}{7} \]

Thus, the correct answer is option (C), \( \frac{3}{7} \).