Question

jeff has 8 red marbles, 6 blue marbles, and 4 green marbles that are the same size and shape. he puts the marbles into a bag, mixes the marbles, and randomly picks one marble. what is the probability that the marble will be blue?
options: \\(\frac{1}{3}\\), \\(\frac{4}{9}\\), \\(\frac{2}{9}\\), \\(\frac{1}{2}\\)

Explanation:

Step1: Calculate total number of marbles

To find the total number of marbles, we add the number of red, blue, and green marbles. So, total marbles \(= 8 + 6 + 4\)
\(= 18\)

Step2: Calculate probability of blue marble

The probability of an event is the number of favorable outcomes (blue marbles) divided by the total number of possible outcomes (total marbles). The number of blue marbles is 6, and total marbles is 18. So, probability \(= \frac{6}{18}\)
Simplify the fraction: \(\frac{6}{18}=\frac{1}{3}\) (Wait, no, wait. Wait, 6 divided by 18: divide numerator and denominator by 6, we get \(\frac{1}{3}\)? Wait, no, 6 and 18 have a common factor of 6? Wait, 6 ÷ 6 = 1, 18 ÷ 6 = 3. Wait, but wait, let's check again. Wait, 8 red, 6 blue, 4 green. Total is 8+6+4=18. Blue marbles: 6. So probability is 6/18 = 1/3? Wait, but let's check the options. One of the options is 1/3. Wait, but wait, maybe I made a mistake. Wait, 6 divided by 18: 6/18 = 1/3. Yes. Wait, but let's check again. 8+6+4=18. Blue is 6. So 6/18 = 1/3. So the probability is 1/3.

Wait, but wait, let's recalculate total marbles: 8 red + 6 blue + 4 green = 18 marbles. Number of blue marbles is 6. So probability of picking a blue marble is number of blue marbles / total number of marbles = 6/18 = 1/3. So the correct option is \(\frac{1}{3}\).

Answer:

\(\frac{1}{3}\) (corresponding to the option with \(\frac{1}{3}\))