You toss a pair of dice. (a) Determine the number of...

Name: Problem 12, Chapter 4: Understandable Statistics, Concepts and Methods
Uploaded: 2021-02-22T14:54:43-08:00
Duration: 58 s
Channel: Hossam Mohamed
Description: You toss a pair of dice. (a) Determine the number of possible pairs of outcomes. (Recall that there are six possible outcomes for each die.) (b) There are three even numbers on each die. How many outcomes are possible with even numbers appearing on each die? (c) Probability extension: What is the probability that both dice will show an even number?

You toss a pair of dice. (a) Determine the number of possible pairs of outcomes. (Recall that there are six possible outcomes for each die.) (b) There are three even numbers on each die. How many outcomes are possible with even numbers appearing on each die? (c) Probability extension: What is the probability that both dice will show an even number?

You toss a pair of dice.
(a) Determine the number of possible pairs of outcomes. (Recall that there are six possible outcomes for each die.)
(b) There are three even numbers on each die. How many outcomes are possible with even numbers appearing on each die?
(c) Probability extension: What is the probability that both dice will show an even number?

Key Concepts

Fundamental Counting Principle

The fundamental counting principle is a basic rule in combinatorics that states if there are m ways to do one thing and n ways to do another, then there are m × n ways of performing both actions in sequence. This concept is essential for determining the total number of outcomes in experiments where choices or events are independent.

Sample Space

The sample space is the set of all possible outcomes of a random experiment. In probability, knowing the sample space is crucial because it forms the basis on which probabilities are assigned to events based on the ratio of favorable outcomes to the total number of outcomes.

Independent Events

Independent events are events where the occurrence of one does not affect the probability of the other occurring. In probability problems involving independent events, such as tossing two dice, the overall probability of a combined event is found by multiplying the probabilities of each individual event.

Event Restriction and Subset Counting

Event restriction and subset counting involve narrowing down the sample space to only those outcomes that satisfy a particular condition or set of conditions. This concept is used to compute probabilities for events defined by specific criteria, such as obtaining certain types of outcomes (for example, only even numbers) on individual runs of an experiment.

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