Ron randomly pulls out a pen of a box that contains one red two black and three blue pens. He does this four times replacing the pen each time, but pulls out a blue pen only one time. Ron concludes that the observed frequency of pulling a blue pen will eventually be closer to the expected frequency, based on the theoretical probability of pulling a pen, which reasons best supports his conclusions
Responses
A. The theoretical probability of pulling a blue pen, based on the expected frequency, will get closer to 1/2 as the number of trials increases
B. The experimental probability of pulling a blue pen based on the
Observed frequency, will get closer to 1/3 as the number of trials increases
C. The theoretical probability of pulling a blue pen based on the expected frequency will get closer to 1/3 as the number of trials increases.
D. The experimental probability of pulling a blue pen based on the
Observed frequency, will get closer to 1/2 as the number of trials increases
B. The experimental probability of pulling a blue pen based on the observed frequency will get closer to 1/3 as the number of trials increases.
The correct answer is D. The experimental probability of pulling a blue pen based on the observed frequency will get closer to 1/2 as the number of trials increases.
In this scenario, the box contains a total of 6 pens: 1 red, 2 black, and 3 blue. Since Ron is replacing the pen after each draw, the probability of pulling a blue pen remains the same for each trial, which is 3/6 or 1/2.
As Ron continues to pull pens from the box, the observed frequency of pulling a blue pen will fluctuate from trial to trial. However, as the number of trials increases, the observed frequency is expected to approach the theoretical probability, which is 1/2. Thus, the experimental probability based on the observed frequency will get closer to 1/2 as the number of trials increases.