Suppose you toss three coins into the air and let them fall...

Suppose you toss three coins into the air and let them fall on the floor. Each coin shows either a head or a tail. a. Make a table in which you list all the possible outcomes of this experiment. Call the coins $\mathrm{A}, \mathrm{B},$ and $\mathrm{C} .$ b. What is the probability of getting two heads and one tail? Explain. c. What is the probability of getting at least two heads?

Suppose you toss three coins into the air and let them fall on the floor. Each coin shows either a head or a tail.
a. Make a table in which you list all the possible outcomes of this experiment. Call the coins $\mathrm{A}, \mathrm{B},$ and $\mathrm{C} .$
b. What is the probability of getting two heads and one tail? Explain.
c. What is the probability of getting at least two heads?

Key Concepts

Combinatorics

Combinatorics is the branch of mathematics dealing with counting, arrangement, and combination of objects. It provides tools, such as combinations and permutations, which are used to count the number of ways a particular event can occur. This is particularly useful when determining the number of favorable outcomes for events with specific criteria, like getting a certain number of heads in coin tosses.

Probability Calculation

Probability calculation involves using the ratio of the number of favorable outcomes for an event to the total number of outcomes in the sample space. This basic principle underpins the computation of probabilities in any experiment and is particularly straightforward in experiments with equally likely outcomes, such as tossing coins.

Event

An event is a collection of one or more outcomes from the sample space that share a particular property. For example, getting two heads and one tail is an event in the context of coin tossing. Clearly defining the event is necessary to determine the number of favorable outcomes needed for calculating the event's probability.

Equally Likely Outcomes

This concept is based on the assumption that each outcome in the sample space has the same chance of occurring. In experiments involving fair coins or other balanced objects, it allows us to assign uniform probabilities to each outcome and calculate probabilities by using ratios of favorable outcomes to the total outcomes.

Outcome

An outcome is a single result from an experiment. When tossing coins, each possible combination of heads or tails represents a distinct outcome. Clearly defining each outcome allows one to precisely count the total number of possibilities, which is essential for determining probabilities.

Sample Space

The sample space refers to the set of all possible outcomes of an experiment. In the context of probability, especially with coin tosses, it includes every combination that can result from the experiment. Defining the sample space is crucial because it forms the basis for calculating probabilities by offering a complete view of the scenario.

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