A bag contains a total of 24 white, red, and blue marbles. A student randomly selects a marble from the bag, records the color, and then returns the marble to the bag. The student repeats the process 24 times. The bar graph shows the results of the student's experiment and the actual number of each color of marble in the bag. Find the theoretical and experimental probability of the event. Give your answer as a reduced fraction and as a decimal rounded to the nearest hundredth.
A randomly selected marble from the bag is blue.
We do not have access to the bar graph.
1/6
To find the theoretical probability of selecting a blue marble, we need to compare the number of blue marbles in the bag to the total number of marbles in the bag.
According to the bar graph, the bag contains a total of 24 marbles. To find the theoretical probability, we need to determine the number of blue marbles in the bag.
Since the bar graph does not provide the exact number of blue marbles, we can estimate it by looking at the graph. Based on the height of the blue bar compared to the other bars, it seems that there are approximately 7 blue marbles.
Therefore, the theoretical probability of selecting a blue marble can be calculated as follows:
Theoretical Probability = Number of Blue Marbles / Total Number of Marbles
Theoretical Probability = 7 / 24
To express this as a reduced fraction, we divide the numerator and denominator by their greatest common divisor, which is 1 in this case:
Theoretical Probability = 7 / 24
To convert this fraction into a decimal, we divide 7 by 24:
Theoretical Probability (decimal) ≈ 0.29 (rounded to the nearest hundredth)
Now, let's also calculate the experimental probability. The experimental probability is determined by conducting the experiment multiple times and recording the outcomes.
According to the experiment, the student repeated the process 24 times. We need to determine how many times a blue marble was selected.
Again, based on the heights of the bars in the graph, it appears that the student selected a blue marble 5 times.
Therefore, the experimental probability of selecting a blue marble can be calculated as follows:
Experimental Probability = Number of Times Blue Marble was Selected / Total Number of Trials
Experimental Probability = 5 / 24
To express this as a reduced fraction, we divide the numerator and denominator by their greatest common divisor, which is 1 in this case:
Experimental Probability = 5 / 24
To convert this fraction into a decimal, we divide 5 by 24:
Experimental Probability (decimal) ≈ 0.21 (rounded to the nearest hundredth)
In summary:
The theoretical probability of selecting a blue marble is 7/24 or approximately 0.29.
The experimental probability of selecting a blue marble is 5/24 or approximately 0.21.