Question

A bag contains 3 red, 5 blue, and 7 green balls. If a ball is drawn at random, what is the probability it is either red or blue?

• A. \( \frac{1}{3} \)
• B. \( \frac{1}{2} \)
• C. \( \frac{2}{3} \)
• D. \( \frac{3}{5} \)
• E. \( \frac{4}{5} \)

Hint:

When finding the probability of multiple outcomes, simply add the number of favorable outcomes together and divide by the total possible outcomes.

Answer 1

The Correct Option is B

Step 1: Find the total number of balls in the bag. The bag contains: \begin{itemize} \item 3 red balls \item 5 blue balls \item 7 green balls \end{itemize} Thus, the total number of balls is: \[ 3 + 5 + 7 = 15 \] Step 2: Find the total number of favorable outcomes (red or blue). The number of favorable outcomes is the total number of red balls plus the total number of blue balls: \[ 3 + 5 = 8 \] Step 3: Calculate the probability. The probability of drawing a red or blue ball is the ratio of favorable outcomes to total outcomes: \[ P(\text{red or blue}) = \frac{8}{15} \] Step 4: Simplify the fraction. The fraction \( \frac{8}{15} \) cannot be simplified further, so the probability is \( \frac{8}{15} \).