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 blue? submit your answer as a simplified fraction, as well as a decimal and percentage, both rounded to the hundredths place. show your work here. fraction: decimal: percent:

Explanation:

Step1: Calculate the total number of marbles

There are \(4\) marbles in total.

Step2: Calculate the number of blue marbles

There are \(2\) blue marbles.

Step3: Calculate the probability as a fraction

The probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So, \(P = \frac{2}{4}=\frac{1}{2}\).

Step4: Convert the fraction to a decimal

To convert \(\frac{1}{2}\) to a decimal, divide \(1\) by \(2\): \(1\div2 = 0.5\).

Step5: Convert the decimal to a percentage

To convert a decimal to a percentage, multiply by \(100\). So, \(0.5\times100 = 50.00\%\).

Answer:

Fraction: \(\frac{1}{2}\)
Decimal: \(0.5\)
Percentage: \(50.00\%\)