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What is the fundamental principle of counting in probability?

Back

The fundamental principle of counting states that if there are 'm' ways to do one thing and 'n' ways to do another, then there are m x n ways to do both.

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How do you calculate the total number of meal combinations from multiple choices?

Back

Multiply the number of choices for each category. For example, if there are 2 salads, 3 entrees, and 2 beverages, the total combinations are 2 x 3 x 2 = 12.

Front

What is a permutation in probability?

Back

A permutation is an arrangement of objects in a specific order. The number of permutations of 'n' objects taken 'r' at a time is given by the formula: P(n, r) = n! / (n - r)!.

Front

How do you calculate the number of ways to choose and arrange items?

Back

To choose and arrange 'r' items from 'n' items, use the permutation formula: P(n, r) = n! / (n - r)!. For example, choosing and arranging 3 songs from 9 gives P(9, 3) = 9! / (9 - 3)! = 504.

Front

What is the probability of an event?

Back

The probability of an event is a measure of the likelihood that the event will occur, calculated as the number of favorable outcomes divided by the total number of possible outcomes.

Front

What is the probability of getting all answers correct on a true/false quiz with 3 questions?

Back

The probability is calculated as (1/2)^3 = 1/8, since each question has 2 possible answers.

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How do you calculate the probability of picking a specific item from a group?

Back

The probability of picking a specific item is calculated as the number of favorable outcomes divided by the total number of outcomes. For example, if there are 2 blue balls in a total of 10 balls, the probability is 2/10 = 1/5.

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What is the formula for calculating combinations?

Back

The formula for combinations is C(n, r) = n! / [r!(n - r)!], where 'n' is the total number of items, and 'r' is the number of items to choose.

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What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not. For example, choosing 2 items from 3 (A, B, C) gives 3 permutations (AB, AC, BA, BC, CA) but only 3 combinations (AB, AC, BC).

Front

What is a sample space in probability?

Back

A sample space is the set of all possible outcomes of a probability experiment. For example, the sample space for flipping a coin is {Heads, Tails}.