Your teacher has a large box containing an equal number of red and blue folders. There are 24 students in your class. The teacher passes out folders at random. Ten students receive a red folder. Compare the experimental probability of recieving a red folder with the theoretical probability of recieving a red folder.
Please help! I'm so confused!
Thanks so much! :)
Don't worry, I'm here to help you understand the concept of experimental and theoretical probability.
Experimental probability is the probability of an event occurring based on actual data or observations. In this case, it refers to the probability of a student receiving a red folder, based on the outcome of the teacher distributing folders randomly.
On the other hand, theoretical probability is the probability of an event occurring based on logical reasoning or mathematical calculations. It is determined by looking at all possible outcomes and the likelihood of each outcome occurring.
To compare the experimental and theoretical probability of receiving a red folder, let's calculate each one step by step:
1. Experimental Probability:
Since there are 24 students in the class, the total number of folders distributed is also 24. Out of those, 10 red folders were given to students.
The experimental probability of receiving a red folder can be calculated by dividing the number of successful outcomes (red folders) by the total number of outcomes (total folders distributed).
Experimental Probability = Number of Red Folders / Total Number of Folders
Plugging in the values:
Experimental Probability = 10 / 24
2. Theoretical Probability:
Theoretical probability can be calculated by dividing the number of favorable outcomes (red folders in this case) by the total number of possible outcomes.
Theoretical Probability = Number of Red Folders / Total Number of Folders
Plugging in the values:
Theoretical Probability = 12 (equal number of red and blue folders) / 24
Now, let's calculate both probabilities:
Experimental Probability = 10 / 24 = 0.4167 (approx.)
Theoretical Probability = 12 / 24 = 0.5
Therefore, the experimental probability of receiving a red folder is approximately 0.4167, while the theoretical probability is 0.5.
By comparing these two probabilities, we can see that the experimental probability is slightly lower than the theoretical probability. This indicates that in the given scenario, the students received slightly fewer red folders than what would be expected based on an equal distribution of red and blue folders.
half are red so p = 1/2 = .5
theory = (1/2)(24) = 12 students get red
experiment = (p exp) (24) = 10
so
p exp = 10/24 = .417 instead of 0.5