3-1 Basic Probability and the Counting Principle

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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, calculated as the number of favorable outcomes divided by the total number of outcomes.

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How do you calculate the theoretical probability of landing on an even number on a spinner with 11 sections?

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The probability is calculated as the number of even sections (5: 2, 4, 6, 8, 10) divided by the total sections (11). So, P(even) = 5/11 ≈ 0.45 or 45%.

Front

What is the theoretical probability of pulling a red marble from a bag containing 3 red, 2 blue, and 4 yellow marbles?

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The probability is calculated as the number of red marbles (3) divided by the total number of marbles (9). So, P(red) = 3/9 = 1/3 or 33%.

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How can probability be expressed?

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Probability can be expressed as a fraction, a decimal, or a percent.

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What is the probability of spinning a fair 8-sided spinner and landing on the number 7?

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The probability is calculated as the number of favorable outcomes (1 for landing on 7) divided by the total outcomes (8). So, P(7) = 1/8.

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If a menu has 6 sandwiches, 3 types of chips, and 5 beverages, how many different lunch combinations can be made?

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The total combinations are calculated by multiplying the number of options: 6 sandwiches x 3 chips x 5 beverages = 90 combinations.

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What is the formula for calculating probability?

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Probability = (Number of favorable outcomes) / (Total number of outcomes).

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What is an example of an impossible event in probability?

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An example of an impossible event is rolling a 7 on a standard 6-sided die.

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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 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 the event is impossible and will not occur.