Regina has a bag of 6 orange marbles and 6 black marbles. She picks a marble at random and then puts it back in the bag. She does this 24 times. The results are shown in the table.
Outcome Tally
Orange 10
Black 14
Determine the percent error of pulling a black marble in Regina’s experiment. Show your work and round your answer to the nearest hundredth.
Since there are 6 blacks and 6 reds, the theoretical probability of pulling a black is 1/2
So in repeating this 24 times, the theoretical result should be 12 orange and 12 blacks
The actual experiment resulted in a prob of 14/24 or 7/12 of pulling a black.
There is really no "error" here, that's just how the results turned out.
If they had asked for the difference between the experimental probability and the theoretical probability, then it would be 7/12 - 1/2 = .... , now change that to a percent
Btw, your question did not state what the base of that "percent error" is, based on exp. prob.
or theor. prob.
are they right?
if so they are the 1st helpful teacher i have seen
To determine the percent error of pulling a black marble in Regina's experiment, we need to compare the observed frequency with the expected frequency.
The expected frequency can be calculated by taking the total number of marbles (12) and multiplying it by the probability of pulling a black marble, which is 6/12 or 0.5.
Expected Frequency = Total Marbles * Probability of Black Marble
Expected Frequency = 12 * 0.5
Expected Frequency = 6
The observed frequency of pulling a black marble in Regina's experiment is given as 14.
Now we can calculate the percent error using the formula:
Percent Error = |(Observed Frequency - Expected Frequency) / Expected Frequency| * 100
Percent Error = |(14 - 6) / 6| * 100
Percent Error = |8 / 6| * 100
Percent Error = (8 / 6) * 100
Percent Error = 1.33 * 100
Percent Error = 133%
Therefore, the percent error of pulling a black marble in Regina's experiment is 133%.
To determine the percent error of pulling a black marble in Regina's experiment, we need to compare the observed proportion of black marbles to the expected proportion.
First, let's calculate the expected proportion. Since Regina has a bag of 6 orange marbles and 6 black marbles, the probability of pulling a black marble is 6/12, which simplifies to 1/2 or 0.5.
Now, let's calculate the observed proportion of black marbles. The table shows that out of 24 draws, Regina pulled 14 black marbles. So the proportion of black marbles is 14/24.
Next, we can calculate the percent error using the formula:
Percent Error = (|Observed Value - Expected Value| / Expected Value) * 100
Substituting the values, we get:
Percent Error = (|14/24 - 1/2| / 1/2) * 100
Simplifying further:
Percent Error = (|14/24 - 12/24| / 12/24) * 100
= (|2/24| / 12/24) * 100
= (2/24) / (12/24) * 100
= 2/12 * 100
= 1/6 * 100
= 16.67
Rounded to the nearest hundredth, the percent error of pulling a black marble in Regina's experiment is approximately 16.67%.