Comparing theoretical to experimental probabilites | 7th grade | Khan Academy

TL;DR

Theoretical probability suggests a 1/2 chance of picking a magenta marble, but experimental results with 10,000 trials show an 80% chance of picking magenta, leading to further investigation.

Transcript

• Let's say that you've got a bag, and in that bag you put a bunch of marbles. So, let's say you put 50 of these magenta marbles. So one, two, three, four, five, six, seven, I'm not gonna draw all of them but you get the general idea. There are going to be 50 magenta marbles, and there's also going to be 50 blue marbles. And what you do is, you hav... Read More

Key Insights

• 🛻 Theoretical probability suggests a 1/2 chance of picking a magenta marble.
• ❓ Experimental results with only 10 trials may not align exactly with the theoretical probability.
• 🌥️ However, with a large number of trials (e.g., 10,000), a significant difference between theoretical and experimental probabilities suggests further investigation.

Questions & Answers

Q: What is the initial theoretical probability of picking a magenta marble?

The initial theoretical probability is 1/2 since there are 50 magenta and 50 blue marbles in the bag, out of a total of 100 marbles.

Q: Why is it reasonable to have a different result after 10 experiments compared to the theoretical probability?

With only 10 experiments, there is enough variation in picking to not always get an exact 1/2 probability. Fluctuations in the number of magenta marbles picked is expected.

Q: Why does the experimental result of picking 8,000 magenta marbles out of 10,000 trials raise concerns?

The experimental probability of 80% is significantly higher than the theoretical probability of 1/2. With a large number of trials, such a deviation is unlikely if the true probability was 1/2.

Q: What are some possible explanations for the difference between theoretical and experimental probabilities?

Possibilities include different weights or textures of the marbles, causing them to settle differently in the bag or affect grip, leading to a higher likelihood of picking a magenta marble.

Summary & Key Takeaways

• The theoretical probability of picking a magenta marble from a bag with 50 magenta and 50 blue marbles is 1/2.

• After 10 experiments, picking 7 magenta and 3 blue marbles is reasonable and does not raise concerns about the theoretical probability.

• However, after 10,000 experiments, picking 8,000 magenta and 2,000 blue marbles suggests a significant difference between experimental and theoretical probabilities.