Theoretical and Experimental Probability

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What is theoretical probability?

Back

Theoretical probability is the likelihood of an event happening based on all possible outcomes, calculated using the formula: P(Event) = Number of favorable outcomes / Total number of outcomes.

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What is experimental probability?

Back

Experimental probability is the likelihood of an event happening based on actual experiments or trials, calculated using the formula: P(Event) = Number of times the event occurs / Total number of trials.

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How do you calculate the probability of an event?

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Probability of an event = Number of favorable outcomes / Total number of possible outcomes.

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What is the theoretical probability of landing on green or red in a spinner with 6 equal sections (2 green, 4 red)?

Back

Theoretical probability = (Number of green + Number of red) / Total sections = (2 + 4) / 6 = 6/6 = 1.

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If a bag contains 5 quarters, 2 dimes, and 4 pennies, what is the probability of picking a quarter?

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Probability of picking a quarter = Number of quarters / Total coins = 5 / (5 + 2 + 4) = 5 / 11.

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What is the theoretical probability of landing on a specific number (e.g., 5) on a spinner with 10 equal sections?

Back

Theoretical probability = Number of favorable outcomes (1 for landing on 5) / Total sections = 1 / 10.

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What is the experimental probability of landing on green or red if it was observed 5 times out of 10 spins?

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Experimental probability = Number of times landing on green or red / Total spins = 5 / 10 = 1/2.

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What is the probability of spinning red if there are 3 red sections on a spinner with 10 equal sections?

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Probability of spinning red = Number of red sections / Total sections = 3 / 10.

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What is the difference between theoretical and experimental probability?

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Theoretical probability is based on expected outcomes, while experimental probability is based on actual results from trials.

Front

If a spinner has 4 sections: 1 green, 2 red, and 1 blue, what is the theoretical probability of landing on red?

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Theoretical probability of red = Number of red sections / Total sections = 2 / 4 = 1/2.