PLEASE HELP!!
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.
expected outcome ...12 / 24
actual outcome ... 14 / 24
% error ... [(actual - expected) / expected] * 100%
thanks
To determine the percent error of pulling a black marble in Regina's experiment, we need to compare the expected probability of pulling a black marble to the observed (experimental) probability.
Expected Probability:
Since Regina has a bag of 6 orange marbles and 6 black marbles, the expected probability of pulling a black marble is given by the ratio of the number of black marbles to the total number of marbles in the bag:
Expected Probability of Pulling a Black Marble = Number of Black Marbles / Total Number of Marbles
= 6 / (6 + 6)
= 6/12
= 1/2
= 0.5
Observed Probability:
From the given table, we see that Regina pulled a black marble 14 times out of 24 total pulls.
Observed Probability of Pulling a Black Marble = Number of Times Black Marble was Pulled / Total Number of Pulls
= 14 / 24
= 0.583333...
Now, let's calculate the percent error using the formula:
Percent Error = | (Observed Probability - Expected Probability) / Expected Probability | * 100
Percent Error = | (0.583333... - 0.5) / 0.5 | * 100
= | 0.083333... / 0.5 | * 100
= | 0.166666... | * 100
= 16.67
Therefore, the percent error of pulling a black marble in Regina's experiment is approximately 16.67%.