Experimental Probability

Summary

This video introduces experimental probability, which is calculated based on the outcomes of an experiment. The formula for experimental probability is the number of times an event occurs divided by the total number of trials. The video uses two examples: spinning a color on a spinner and catching a pencil flip. It demonstrates how to calculate the probability of these events and how to use the results to predict outcomes in similar future experiments. The video also guides viewers on how to use a website to simulate spinning a spinner and encourages them to try the examples on their own.

Takeaways

• 🔬 Experimental probability is calculated based on the outcomes of an experiment.
• 🎯 The formula for experimental probability is the number of times an event occurs divided by the total number of trials.
• 🌐 A useful website, nctm, allows users to simulate spinning a customized spinner and skip to the end to see results.
• 📊 For the spinner example, the probability of landing on blue is calculated by dividing the number of times blue was landed on (8 times) by the total spins (50 times), simplifying to 4/25.
• 📈 The probability can be expressed as a fraction (4/25), a percentage (16%), or a decimal (0.16).
• 🤔 The second example involves flipping a pencil and catching it, with an experimental probability of catching calculated from 10 trials resulting in 7 catches.
• 📉 The pencil-flip experiment's results can be used to predict the number of catches in 50 flips by multiplying the experimental probability (7/10) by 50.
• 🧮 Multiplication is used to scale the experimental probability from a smaller experiment (10 flips) to a larger one (50 flips), resulting in an expected 35 catches.
• 📚 The video script is part one of a two-part lesson, with part two focusing on theoretical probability.

Q & A

What is experimental probability?

Experimental probability is a probability that is determined based on the results of an experiment. It is calculated by dividing the number of times an event occurs by the total number of trials.

How many times was the spinner spun in the example provided?

In the example provided, the spinner was spun 50 times.

What is the experimental probability of spinning a blue section on the spinner?

The experimental probability of spinning a blue section on the spinner is 8/50, which simplifies to 4/25 or 16%.

What website was mentioned for simulating the spinner?

The website mentioned for simulating the spinner is nctm, where you can customize your own spinner and perform experiments without physically spinning it.

How many pencil flips did the presenter catch out of 10 in the example?

The presenter caught 7 out of 10 pencil flips in the example.

What is the experimental probability of catching a pencil flip based on the example?

The experimental probability of catching a pencil flip is 7/10 or 70%.

How many pencil flips should the presenter expect to catch out of 50, based on the experimental probability?

Based on the experimental probability, the presenter should expect to catch approximately 35 out of 50 pencil flips.

What is the formula to calculate experimental probability?

The formula to calculate experimental probability is (Number of times the event occurs) / (Total number of trials).

Why is it useful to calculate experimental probability?

Calculating experimental probability is useful because it allows us to make predictions about future events based on past observations.

What is the difference between experimental probability and theoretical probability?

Experimental probability is based on observed outcomes from actual experiments, while theoretical probability is based on the inherent properties of a system and assumes a large number of trials.

How can the presenter's pencil flip results be used to predict future outcomes?

The presenter's pencil flip results can be used to predict future outcomes by using the experimental probability as an estimate of the likelihood of catching a pencil flip in future attempts.