Question

the following set of marbles is placed into a bag. then, without looking, a marble is pulled out of the bag. what is the probability that the chosen marble will be yellow? submit your answer as a simplified fraction, as well as a decimal and percentage, both rounded to the hundredths place.

Explanation:

Step1: Calculate total number of marbles

There are \(3\) dark - colored marbles \(+ 3\) blue marbles \(+ 1\) yellow marble. So total marbles \(n = 3 + 3+1=7\).

Step2: Use probability formula

Probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Number of favorable outcomes (yellow marbles) \(m = 1\). So fraction \(P=\frac{1}{7}\).

Step3: Convert fraction to decimal

\(\frac{1}{7}=1\div7\approx0.14\) (rounded to hundredths place).

Step4: Convert decimal to percentage

Multiply decimal by \(100\). \(0.14\times100 = 14.29\%\) (rounded to hundredths place).

Answer:

Fraction: \(\frac{1}{7}\), Decimal: \(0.14\), Percentage: \(14.29\%\)