Learn on PengiReveal Math, AcceleratedUnit 10: Probability

Lesson 10-2: Experimental Probability of Simple Events

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 10: Probability), students learn how to calculate experimental probability of simple events by finding the ratio of the number of times an event occurs to the total number of trials. Students also use experimental probability to predict relative frequency through proportional reasoning, and explore why an experimental probability of zero does not mean an event is impossible.

Section 1

Calculating Experimental Probability

Property

Experimental probability is based on the actual results of an experiment. It is calculated as

P(extevent)=Number of times event occursTotal number of trialsP( ext{event}) = \frac{\text{Number of times event occurs}}{\text{Total number of trials}}

Examples

  • If you flip a coin 20 times and get 12 heads, the experimental probability of heads is 1220\frac{12}{20}, or 35\frac{3}{5}.
  • Our sample simulation of 3 trials had 2 winners, so the experimental probability was P(extatleastonewinner)=23P( ext{at least one winner}) = \frac{2}{3}.
  • A player makes 8 out of 10 free throws. Their experimental probability of making a shot is 810\frac{8}{10}.

Explanation

This is probability in the wild! It’s the result you get from actually doing an experiment, like your spinner simulation. It’s what happened, not what should have happened. The more trials you do, the more reliable this result becomes.

Section 2

Using Experimental Probability to Predict Expected Counts

Property

You can use the experimental probability of an event to predict the expected number of times the event will occur in a different number of trials.

Expected Count=Experimental Probability×Total Future Trials\text{Expected Count} = \text{Experimental Probability} \times \text{Total Future Trials}

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Calculating Experimental Probability

Property

Experimental probability is based on the actual results of an experiment. It is calculated as

P(extevent)=Number of times event occursTotal number of trialsP( ext{event}) = \frac{\text{Number of times event occurs}}{\text{Total number of trials}}

Examples

  • If you flip a coin 20 times and get 12 heads, the experimental probability of heads is 1220\frac{12}{20}, or 35\frac{3}{5}.
  • Our sample simulation of 3 trials had 2 winners, so the experimental probability was P(extatleastonewinner)=23P( ext{at least one winner}) = \frac{2}{3}.
  • A player makes 8 out of 10 free throws. Their experimental probability of making a shot is 810\frac{8}{10}.

Explanation

This is probability in the wild! It’s the result you get from actually doing an experiment, like your spinner simulation. It’s what happened, not what should have happened. The more trials you do, the more reliable this result becomes.

Section 2

Using Experimental Probability to Predict Expected Counts

Property

You can use the experimental probability of an event to predict the expected number of times the event will occur in a different number of trials.

Expected Count=Experimental Probability×Total Future Trials\text{Expected Count} = \text{Experimental Probability} \times \text{Total Future Trials}