Question

instructions
solve the following problem and choose the best answer.
question
a bag contains 15 red candies, 15 yellow candies, and 15 blue candies. what is the probability of randomly choosing two candies of the same color, without replacement?
$\frac{1}{3}$
$\frac{1}{9}$
$\frac{7}{22}$
$\frac{1}{15}$

Explanation:

Step1: Calculate total number of candies

Total candies \(=15 + 15+15=45\)

Step2: Calculate probability for one - color pair (e.g., red)

Probability of first red candy \(=\frac{15}{45}\), probability of second red candy (without replacement) \(=\frac{14}{44}\). Probability for red pair \(=\frac{15}{45}\times\frac{14}{44}\)

Step3: Multiply by 3 (for red, yellow, blue)

Since there are 3 colors, total probability \(=3\times\frac{15}{45}\times\frac{14}{44}\)

$$
LATEXBLOCK0
$$

Answer:

\(\frac{7}{22}\)