Nikita performed an experiment in which she randomly pulled a marble from a bag, recorded its color, placed it back in the bag, and then repeated. The results are shown in the following table.

Question

Result Frequency
Red 20
Purple 24
Blue 12

Based on the experiment, what is the probability of drawing a blue marble?

Enter your answer as a fraction, like this: 42/53

Answer 1

To find the probability of drawing a blue marble, we first need to calculate the total frequency of all the marbles.

The total frequency is the sum of the frequencies of all the colors:

\[ \text{Total frequency} = \text{Red} + \text{Purple} + \text{Blue} = 20 + 24 + 12 = 56 \]

Now, the probability of drawing a blue marble is given by the frequency of blue marbles divided by the total frequency:

\[ \text{Probability of blue} = \frac{\text{Frequency of blue}}{\text{Total frequency}} = \frac{12}{56} \]

Next, we can simplify this fraction. We can divide both the numerator and the denominator by their greatest common divisor, which is 4:

\[ \frac{12 \div 4}{56 \div 4} = \frac{3}{14} \]

Thus, the probability of drawing a blue marble is:

\[ \boxed{\frac{3}{14}} \]