Question

Consider the following experiment: toss a coin twice and record the sequence of heads and tails. Calculate the probability of the event in Exercise $3 .$

   Consider the following experiment: toss a coin twice and record the sequence of heads and tails.
Calculate the probability of the event in Exercise $3 .$

Precalculus : Building Concepts and Connections

Precalculus : Building Concepts and Connections

Revathi Narasimhan 1st Edition

Chapter 10, Problem 4

Instant Answer

Solved by Expert Charles Carter

04/18/2020

Step 1

In this case, we are tossing a coin twice and recording the sequence of heads and tails. The possible outcomes are: Head-Head (HH), Head-Tail (HT), Tail-Head (TH), and Tail-Tail (TT). So, the sample space is {HH, HT, TH, TT}. Show more…

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Consider the following experiment: toss a coin twice and record the sequence of heads and tails. Calculate the probability of the event in Exercise $3 .$

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Key Concepts

Outcome Enumeration

Outcome enumeration is the process of listing all possible outcomes of an experiment in order to analyze and compare them. This systematic approach is essential in problems like coin toss experiments to ensure that all potential outcomes are considered in probability calculations.

Event Probability

Event probability involves determining the likelihood of an event by identifying favorable outcomes and comparing them to the total number of outcomes. This concept is central when calculating probabilities for events defined within the sample space.

Independent Events

Independent events are occurrences where the outcome of one event does not affect the outcome of another. In a two-coin toss experiment, the result of the first toss does not influence the result of the second toss, a key point when calculating overall probabilities.

Sample Space

The sample space is the complete set of all possible outcomes for an experiment. In the context of coin tosses, it refers to listing every possible result, such as heads or tails combinations when the coin is tossed twice.

Uniform Probability Distribution

A uniform probability distribution means that each outcome in the sample space has an equal chance of occurring. With a fair coin, each toss yields heads or tails with equal probability, simplifying the calculation of the probability of any event.

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