Chapter 4 Probability Question and Answer 2023.
Key Concepts Correct Answer: The single most important objective of this section is to learn how to
... [Show More] interpret probability values, which are expressed as values between 0 and 1. A small probability, such as 0.001, corresponds to an event that rarely occurs.
Next are odds and how they relate to probabilities. Odds are commonly used in situations such as lotteries and gambling.
Basics of Probability Correct Answer: Notation for Probabilities
P denotes a probability.
A, B, and C denote specific events.
P(A) denotes the "probability of event A occurring."
Probability Limits Correct Answer: For any event A, the probability of A is between 0 and 1 inclusive: 0 ≤ P(A) ≤ 1.
• The probability of an impossible event is 0.
• The probability of a event that is certain to occur is 1.
Example:
Using a standard 6-sided die, find:
• P(rolling a number greater than 7) = 0 • P(rolling a number less than 7) = 1
Common Expressions of Likelihood Correct Answer: Possible values of probabilities and the more familiar and common expressions of likelihood.
Unlikely Events Correct Answer: Unless stated otherwise, consider an event to be unlikely, unusual, or significant if its probability is less than or equal to 0.05.
Example 1: Relative Frequency
Approach. Correct Answer: Rounding Probabilities
When expressing the value of a probability, either give the exact fraction or decimal or round off final decimal results to three significant digits.
Approaches to Probability. Correct Answer: • Relative Frequency Approximation of Probability
• Classical Approach to Probability
• Subjective Probability
- The probability of an event is estimated by using
knowledge of the relevant circumstances.
• Simulations
- Sometimes none of the preceding three approaches can
be used. A simulation of a procedure is a process that
behaves in the same ways as the procedure itself so that
similar results are produced. Probabilities can sometimes be found by using a simulation.
Relative Frequency Approximation of Probability Correct Answer: Conduct (or observe) a procedure and count the
number of times that event A occurs. P(A) is then approximated as follows:
Example #1 Correct Answer: In a recent year, there were about 3,000,000 skydiving
jumps and 21 of them resulted in deaths.
Find the probability of dying when making a skydiving jump.
Solution
We use the relative frequency approach as follows:
Example # 2 Correct Answer: In a study of U.S. high school drivers, it was found that 3785
texted while driving during the previous 30 days, and 4720
did not text while driving during that same time period.
Based on these results, if a high school driver is randomly
selected, find the probability that he or she texted while
driving during the previous 30 days.
Example #2 Correct Answer: Solution
We can now use the relative frequency approach as follows:
There is a 0.445 probability that if a high school driver is
randomly selected, he or she texted while driving during the
previous 30 days.
Your Turn 1: Relative Frequency Approach. Correct Answer: Use the following table to find the probability of a false positive.
Formula separate. Correct Answer: Classical Approach to Probability (Requires Equally Likely Outcomes) If a procedure has n different simple events that are equally likely, and if event A can occur in s different ways, then. [Show Less]