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Nadia has 5 red cubes, 3 blue cubes, 8 yellow cubes, and 4 black cubes.

She records the color cube she pulls from the bag and puts the cube back in the bag 14 times.

The table below shows the frequency she pulled each color.

What are the experimental and theoretical probability of pulling a blue cube out of the bag? Enter your answer as a decimal rounded to the nearest hundredth (2 places after the decimal).

When entering responses, remember to include the ZERO before the decimal if necessary. For example, if the answer is 0.47, you must enter the zero for the answer to be counted correctly.

(2 points)
Theoretical P(blue) =
Remember to round your answer to the nearest hundredth.

Experimental P(blue) =
Remember to round your answer to the nearest hundredth.

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1 answer

To calculate the theoretical and experimental probabilities, we first need to understand each concept:

  1. Theoretical Probability: This is calculated based on the possible outcomes in a situation, before any actual experiment is conducted.

  2. Experimental Probability: This is calculated based on actual results from an experiment.

Step 1: Calculate the Theoretical Probability of pulling a blue cube.

Total Number of Cubes:

\[ \text{Total cubes} = \text{Red} + \text{Blue} + \text{Yellow} + \text{Black} = 5 + 3 + 8 + 4 = 20 \]

Number of Blue Cubes: \[ \text{Number of blue cubes} = 3 \]

Theoretical Probability of pulling a blue cube (P(blue)): \[ P(blue) = \frac{\text{Number of blue cubes}}{\text{Total number of cubes}} = \frac{3}{20} = 0.15 \]

Step 2: Calculate the Experimental Probability of pulling a blue cube.

If Nadia pulled a cube 14 times and, for example, let’s say she recorded that she pulled a blue cube 2 times, the experimental probability would be calculated as follows:

\[ \text{Number of times blue was pulled (hypothetical)} = 2 \]

Experimental Probability of pulling a blue cube (P(blue)): \[ P(blue)_{experimental} = \frac{\text{Number of times blue was pulled}}{\text{Total pulls}} = \frac{2}{14} = \frac{1}{7} \approx 0.14 \]

Final Answer Formatting (assuming Nadia pulled blue 2 times in the experiment):

  • Theoretical P(blue) = 0.15
  • Experimental P(blue) = 0.14

Note: Please replace "2" in the experimental calculation with the actual frequency if it’s different in the example you provided. The P(blue) values should be rounded to two decimal places as requested.