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. Skip to navigation
To calculate the theoretical probability of pulling a blue cube out of the bag, we need to consider the total number of cubes and the number of blue cubes.
Total number of cubes = 5 (red) + 3 (blue) + 8 (yellow) + 4 (black) = 20 cubes
Number of blue cubes = 3
Theoretical P(blue) = Number of blue cubes / Total number of cubes
Theoretical P(blue) = 3 / 20
Theoretical P(blue) = 0.15
To calculate the experimental probability of pulling a blue cube out of the bag, we use the data from Nadia's 14 pulls:
Number of times blue cube was pulled = 2
Experimental P(blue) = Number of times blue cube was pulled / Total number of pulls
Experimental P(blue) = 2 / 14
Experimental P(blue) = 0.14
Therefore, the theoretical probability of pulling a blue cube out of the bag is 0.15 and the experimental probability is 0.14.