Theoretical & Experimental Probability

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What is Theoretical Probability?

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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?

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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 rolling a specific number on a fair 6-sided die?

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The probability of rolling a specific number (e.g., 4) on a fair 6-sided die is 1/6, since there is one favorable outcome and six possible outcomes.

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If a die is rolled 90 times and the number 1 appears 13 times, what is the experimental probability of rolling a 1?

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The experimental probability of rolling a 1 is 13/90.

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What is the probability of rolling an even number on a fair 6-sided die?

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The probability of rolling an even number (2, 4, or 6) is 3/6 or 1/2.

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If Jane rolled a number cube 25 times and got an even number 11 times, what is the experimental probability of rolling an even number?

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The experimental probability of rolling an even number is 11/25.

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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.

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If a fair number cube is rolled 20 times and the number 4 is rolled 6 times, what is the experimental probability of rolling a 4?

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The experimental probability of rolling a 4 is 6/20 or 3/10.

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Which is greater: the theoretical probability of rolling a 4 (1/6) or the experimental probability of rolling a 4 (3/10)?

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The experimental probability of 3/10 is greater than the theoretical probability of 1/6.

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What is the theoretical probability of rolling an odd number on a fair 6-sided die?

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The theoretical probability of rolling an odd number (1, 3, or 5) is 3/6 or 1/2.