Theoretical and 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 selecting a specific item from a group?

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To calculate the probability of selecting a specific item, use the formula: P(Item) = Number of specific items / Total number of items.

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If a coin is flipped 10 times and lands heads up 6 times, what is the experimental probability of landing heads?

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The experimental probability of landing heads is P(Heads) = 6/10 = 0.6 or 60%.

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What is the probability of selecting a yellow tennis ball from a basket containing 40 yellow and 35 white tennis balls?

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P(Yellow) = 40 / (40 + 35) = 40 / 75 = 0.533 or 53.3%.

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What does it mean if an event has a probability of 1?

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If an event has a probability of 1, it means that the event is certain to occur.

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What does it mean if an event has a probability of 0?

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If an event has a probability of 0, it means that the event is impossible and will not occur.

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What is the law of large numbers in probability?

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The law of large numbers states that as the number of trials increases, the experimental probability will get closer to the theoretical probability.

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If a bag contains 4 different bills and one is drawn at random, what is the probability of drawing a $1 bill?

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P($1) = 1/4 = 0.25 or 25%.

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What should you consider when interpreting the results of a probability experiment?

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Consider the number of trials, the outcomes, and whether the results align with theoretical expectations.