Bob is moving and all of his sports cards are mixed up in a...

Bob is moving and all of his sports cards are mixed up in a box. Twelve cards are baseball, eight are football, and five are basketball. If he reaches in the box and selects them at random, find each probability.

P(2 football, 1 hockey)

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Key Concepts

Probability Basics

Probability is a measure of how likely an event is to occur, calculated as the ratio of the number of favorable outcomes to the total number of outcomes in the sample space. It lays the foundation for analyzing random events, including drawing cards from a mixed set.

Combinatorics

Combinatorics is the branch of mathematics that deals with counting, arranging, and selecting objects. It provides the tools, such as combinations and permutations, which are essential for determining the number of ways events can occur without explicitly listing each possible outcome.

Combination Formula

The combination formula, often written as 'n choose k', is used to calculate the number of ways to choose k items from a set of n items without regard to the order. This concept is key when determining probabilities in scenarios where order does not matter, such as selecting cards from a set.

Feasibility of Outcomes

Feasibility of outcomes examines whether the event being considered can actually occur given the conditions of the problem. When an event requires selecting an item that does not exist in the sample space, the probability of that event is zero, since there are no favorable outcomes to count.

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