Experimental and Theoretical probability

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What is experimental probability?

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Experimental probability is the ratio of the number of times an event occurs to the total number of trials conducted. It is calculated using the formula: P(event) = (Number of times event occurs) / (Total number of trials).

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What is theoretical probability?

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Theoretical probability is the likelihood of an event occurring based on all possible outcomes in a perfect scenario. It is calculated using the formula: P(event) = (Number of favorable outcomes) / (Total number of possible outcomes).

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How do you calculate the experimental probability of rolling a specific number on a die?

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To calculate the experimental probability of rolling a specific number, divide the number of times that number was rolled by the total number of rolls. For example, if you roll a die 10 times and get a 3 three times, the experimental probability of rolling a 3 is 3/10.

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If a bag contains 4 green marbles, 3 red marbles, 2 blue marbles, and 1 yellow marble, what is the theoretical probability of pulling a red marble?

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The theoretical probability of pulling a red marble is calculated as follows: P(red) = (Number of red marbles) / (Total number of marbles) = 3 / (4 + 3 + 2 + 1) = 3/10.

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What is the formula for calculating the probability of picking a rock song or a pop song from a collection?

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To calculate the probability of picking a rock song or a pop song, use the formula: P(rock or pop) = (Number of rock songs + Number of pop songs) / (Total number of songs). For example, if there are 2 rock songs and 11 pop songs, P(rock or pop) = (2 + 11) / (4 + 11 + 8 + 2) = 13/25.

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What is the theoretical probability of a spinner landing on a specific number?

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The theoretical probability of a spinner landing on a specific number is calculated as: P(number) = (Number of sections with that number) / (Total number of sections on the spinner).

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How do you determine the experimental probability of a number appearing on a die after multiple rolls?

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To determine the experimental probability of a number appearing on a die, count how many times that number appears in the results and divide by the total number of rolls. For example, if a number appears 13 times in 90 rolls, the experimental probability is 13/90.

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What is the total number of outcomes when rolling a 6-sided die?

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The total number of outcomes when rolling a 6-sided die is 6, as there are six faces numbered from 1 to 6.

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If a spinner has 8 equal sections numbered 1 to 8, what is the theoretical probability of landing on a 5?

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The theoretical probability of landing on a 5 is P(5) = 1/8, since there is 1 favorable outcome (landing on 5) out of 8 possible outcomes.

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What is the difference between experimental and theoretical probability?

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Experimental probability is based on actual experiments and observed outcomes, while theoretical probability is based on expected outcomes in a perfect scenario.