Mathematics
Grade 7
15 min
Experimental probability
Experimental probability
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Introduction & Learning Objectives
Learning Objectives
Define experimental probability and distinguish it from theoretical probability.
Calculate the experimental probability of an event based on observed data from an experiment.
Interpret the results of probability experiments and express them as fractions, decimals, or percentages.
Compare experimental probability to theoretical probability and explain potential differences.
Use experimental probability to make predictions about future outcomes in similar experiments.
Understand how the number of trials affects the reliability of experimental probability.
Ever wonder how many times a coin *actually* lands on heads if you flip it 100 times? 🪙 Sometimes what we expect isn't exactly what we get!
In this lesson, you'll learn about experimental proba...
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Key Concepts & Vocabulary
TermDefinitionExample
ExperimentA process or activity with an uncertain outcome that can be repeated.Flipping a coin, rolling a die, spinning a spinner, or drawing a card from a deck.
TrialA single performance of an experiment.One flip of a coin is a trial. If you flip a coin 10 times, you have performed 10 trials.
OutcomeA possible result of a single trial of an experiment.When rolling a standard six-sided die, the outcomes are 1, 2, 3, 4, 5, or 6.
EventA specific outcome or a set of specific outcomes that you are interested in.When rolling a die, getting an 'even number' (2, 4, or 6) is an event. Getting a '3' is also an event.
Frequency (of an event)The number of times a specific event occurs during an experiment.If you flip a coin 20 times and it lands on heads 12...
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Core Formulas
Formula for Experimental Probability
$$P(\text{event}) = \frac{\text{Number of times the event occurs}}{\text{Total number of trials}}$$
This formula is used to calculate the experimental probability of a specific event. You count how many times your desired event happened and divide it by the total number of times you performed the experiment.
Predicting Future Outcomes
$$\text{Predicted occurrences} = \text{Experimental Probability} \times \text{Total future trials}$$
Once you've calculated the experimental probability of an event, you can use it to predict approximately how many times that event might occur in a new, larger set of trials. Multiply the experimental probability (as a fraction or decimal) by the total number of future trials.
4 more steps in this tutorial
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Challenging
Two experiments are conducted. Experiment A: A die is rolled 30 times, with '6' appearing 8 times. Experiment B: A die is rolled 300 times, with '6' appearing 55 times. Which experiment's result is likely closer to the theoretical probability, and why?
A.Experiment A, because the probability (8/30) is a simpler fraction.
B.Experiment B, because it has a larger number of trials.
C.Both are equally reliable because they use the same die.
D.Experiment A, because 8 is closer to 6 than 55 is.
Challenging
A spinner with 4 equal sections (A, B, C, D) is spun 120 times. The results are: A=45, B=25, C=26, D=24. Which is the most reasonable conclusion based on this data?
A.The spinner is definitely unfair because the results are not exactly 30 for each section.
B.The results are impossible for a fair spinner.
C.The experimental probability for A is significantly higher than its theoretical probability, which might suggest the spinner is unfair.
D.The experiment must be redone because the total is not a multiple of 4.
Challenging
A factory produces light bulbs. On Monday, 500 bulbs were tested and 15 were defective. On Tuesday, 700 bulbs were tested and 21 were defective. A manager claims the defect rate on Monday was worse than on Tuesday. Based on experimental probability, is this claim accurate?
A.Yes, because fewer bulbs were tested on Monday.
B.Yes, because 15 is less than 21.
C.No, because more bulbs were defective on Tuesday.
D.No, because the experimental probability of a defect was the same on both days.
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