Tossing Three Coins. Three coins are flipped. An outcome...

Tossing Three Coins. Three coins are flipped. An outcome might be HTH.
a) Find the sample space.
What is the probability of getting each of the following?
b) Exactly one head
c) At most two tails
d) At least one head
e) Exactly two tails

Key Concepts

Sample Space

The sample space in probability theory is the set of all possible outcomes of an experiment. In the context of tossing coins, it includes every combination of heads and tails that can appear, serving as the universal set upon which probabilities for events are defined.

Uniform Probability Model

A uniform probability model assumes that each outcome in the sample space has an equal likelihood of occurring. This is particularly useful in problems such as coin tossing, where the fairness of the coins implies that every outcome is equally probable.

Combinatorial Counting

Combinatorial counting involves determining the number of ways events can occur, often using multiplication principles or binomial coefficients. This is essential when calculating probabilities for events defined by specific counts of outcomes, such as exactly one head or exactly two tails.

Binomial Probability

Binomial probability refers to the use of the binomial theorem or formula to calculate the probability of achieving a certain number of successes in a fixed number of independent trials. In coin toss experiments, 'heads' can be seen as successes, and the binomial formula gives the probability of obtaining a specified number of heads.

Complement Rule

The complement rule is a useful concept in probability which states that the probability of an event occurring is one minus the probability of it not occurring. This is particularly helpful in problems involving 'at least' outcomes, such as finding the probability of getting at least one head by subtracting the probability of getting no heads from one.

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