Felix has a bag of 6 yellow marbles and 6 green marbles. He picks a marble and then puts it back 26 times. The results are shown in the table. Yellow 15 and green 11. What is the percent error of pulling a yellow marble in Felix’s experiment?
Thank you
To calculate the percent error of pulling a yellow marble in Felix's experiment, we need to determine the expected probability of pulling a yellow marble and compare it to the observed outcome.
Step 1: Find the expected probability of pulling a yellow marble.
Felix has a bag of 6 yellow marbles and 6 green marbles, so the total number of marbles is 6 + 6 = 12.
The probability of pulling a yellow marble is the number of yellow marbles divided by the total number of marbles: 6/12 = 1/2 = 0.5.
Step 2: Calculate the observed probability of pulling a yellow marble.
From the table, it is given that Felix pulled a yellow marble 15 times out of 26 total pulls.
The observed probability of pulling a yellow marble is the number of times a yellow marble was pulled divided by the total number of pulls: 15/26 ≈ 0.577.
Step 3: Calculate the percent error.
The percent error formula is given by:
Percent Error = |(Observed Value - Expected Value) / Expected Value| * 100
Substituting the values, we have:
Percent Error = |(0.577 - 0.5) / 0.5| * 100
Percent Error = |0.077 / 0.5| * 100
Percent Error = 0.154 * 100
Percent Error = 15.4%
Therefore, the percent error of pulling a yellow marble in Felix's experiment is 15.4%.
To find the percent error of pulling a yellow marble in Felix's experiment, we need to determine the expected probability of pulling a yellow marble.
In Felix's bag, there are 6 yellow marbles and 6 green marbles, totaling 12 marbles. Since Felix picks a marble and then puts it back, the probability of picking a yellow marble remains constant throughout the experiment.
The expected probability of picking a yellow marble can be calculated by dividing the number of yellow marbles by the total number of marbles:
Expected probability of picking a yellow marble = (Number of yellow marbles) / (Total number of marbles)
Expected probability of picking a yellow marble = 6 / 12 = 0.5 or 50%
Now, let's calculate the percent error using the formula:
Percent Error = (Observed value - Expected value) / Expected value * 100
In this case, the observed value is 15 (as given in the table), and the expected value is 50%.
Percent Error = (15 - 50%) / 50% * 100
Simplifying, we get:
Percent Error = -35 / 0.50 * 100
Percent Error = -70%
Therefore, the percent error of pulling a yellow marble in Felix's experiment is -70%.