Question

a marble is randomly selected from a bag of solid - colored marbles. the probability of selecting a red marble is \\(\frac{5}{18}\\). the probability of selecting a black marble is \\(\frac{7}{18}\\). what is the probability of selecting a red or black marble?\\(\bigcirc\\ \frac{35}{324}\\)\\(\bigcirc\\ \frac{1}{3}\\)\\(\bigcirc\\ \frac{2}{3}\\)\\(\bigcirc\\ \frac{5}{9}\\)\\(\bigcirc\\) cannot be determined

Explanation:

Step1: Identify Probability Rule

For mutually exclusive events (a marble can't be both red and black), use \( P(A \cup B) = P(A) + P(B) \).

Step2: Substitute Values

\( P(\text{red or black}) = \frac{5}{18} + \frac{7}{18} \)

Step3: Add Fractions

\( \frac{5 + 7}{18} = \frac{12}{18} \)

Step4: Simplify Fraction

\( \frac{12}{18} = \frac{2}{3} \)

Answer:

\(\frac{2}{3}\) (corresponding to the option with \(\frac{2}{3}\))