ProbabilityLesson 1 of 4 in the course Probability Topics

Probability Events, Complements, and Conditional Probability

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

Probability gives us a way to describe how likely outcomes are in an experiment. This lesson introduces the language used to describe chance experiments and explains how to calculate probabilities when outcomes are equally likely.

An experiment is a planned operation carried out under controlled conditions. When its result is not predetermined, it is a chance experiment. Flipping a fair coin twice is a chance experiment because the particular results cannot be known in advance.

All flashcards

What is a chance experiment?
A controlled operation whose result is not predetermined.
What is an event in probability?
A set of outcomes from a sample space.
How is an event's probability calculated when all outcomes are equally likely?
Divide the number of outcomes in the event by the total number of outcomes in the sample space.
What does the union A∪BA \cup B contain?
Outcomes in AA, in BB, or in both.
What does P(A∣B)P(A \mid B) mean?
The probability of AA given that BB has occurred.

Quiz questions

  1. A fair six-sided die is rolled. Let A={2,3}A = \{2, 3\} and B={2,4,6}B = \{2, 4, 6\}. What is P(A∣B)P(A \mid B)?Answer: 1/31/3
  2. If P(A)=0.35P(A) = 0.35, what is P(A′)P(A')?Answer: 0.650.65
  3. For which sample space can the equally likely counting rule be used directly?Answer: One in which every outcome has the same probability.
  4. A coin lands heads in 56% of 250 flips. What does this result establish about the coin?Answer: The observed result alone does not prove that the coin is biased.
  5. What condition must hold for the formula P(A∣B)=P(A∩B)/P(B)P(A \mid B) = P(A \cap B)/P(B) to apply?Answer: P(B)>0P(B) > 0

Based on Introductory Statistics 2e by Barbara Illowsky, Susan Dean (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

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