Theoretical Probability Practice

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What is theoretical probability?

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Theoretical probability is the likelihood of an event occurring based on the possible outcomes in a perfect world, calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes.

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How do you calculate the probability of a single event?

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The probability of a single event is calculated using the formula: P(A) = Number of favorable outcomes / Total number of possible outcomes.

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What is the probability of rolling a 3 on a standard six-sided die?

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The probability of rolling a 3 on a standard six-sided die is 1/6, since there is one favorable outcome (rolling a 3) and six possible outcomes (1, 2, 3, 4, 5, 6).

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What is the sum of probabilities for all possible outcomes of a random experiment?

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The sum of probabilities for all possible outcomes of a random experiment is always equal to 1.

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What is the difference between theoretical probability and experimental probability?

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Theoretical probability is based on the expected outcomes in a perfect scenario, while experimental probability is based on the actual results obtained from conducting an experiment.

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How do you find the probability of two independent events occurring?

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The probability of two independent events A and B occurring is found by multiplying their individual probabilities: P(A and B) = P(A) * P(B).

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What is a sample space in probability?

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A sample space is the set of all possible outcomes of a random experiment.

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What is the probability of drawing a heart from a standard deck of cards?

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The probability of drawing a heart from a standard deck of 52 cards is 13/52, or 1/4, since there are 13 hearts in the deck.

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What is the concept of complementary events in probability?

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Complementary events are two outcomes of an event that are mutually exclusive and together cover all possible outcomes. The probability of an event and its complement always adds up to 1.

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How do you calculate the probability of at least one event occurring?

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To calculate the probability of at least one event occurring, you can use the formula: P(at least one) = 1 - P(none).