5.1 Probability Concepts

• A probability of 0 means the event is impossible.


  True
• A probability of 0 indicates an impossible event.

  True
• Theoretical probability is based on mathematical models.


  True
• How many main types of probability are there?

  Three
• What is an example of empirical probability?

  Rolling a 6 on a fair die based on many trials
• Subjective probability is based on personal judgment, experience, or beliefs
• What is the calculation for empirical probability?

  Ratio of favorable outcomes to total outcomes
• What does P(A) represent in probability notation?

  Probability of event A occurring
• A probability of 1 means the event is certain
• Order the likelihood of events based on their probability values from least likely to most likely.

  1️⃣ 0 ||| Impossible

  2️⃣ 0.25 ||| Unlikely

  3️⃣ 0.5 ||| Equally likely to occur or not occur

  4️⃣ 0.75 ||| Likely

  5️⃣ 1 ||| Certain
• Match the type of probability with its definition.

  Empirical ↔️ Based on observed data

  Theoretical ↔️ Based on mathematical models

  Subjective ↔️ Based on personal judgment
• Empirical probability is based on observed data or experiments.


  True
• Theoretical probability is calculated using the total number of possible outcomes
• Match the type of probability with its definition, calculation, and example:

  Empirical ↔️ Based on observed data ||| Ratio of favorable outcomes to total outcomes ||| Rolling a 6 on a die based on many trials

  Theoretical ↔️ Based on mathematical models ||| Total favorable outcomes / Total possible outcomes ||| Rolling a 6 on a fair die is 1/6

  Subjective ↔️ Based on personal judgment ||| Not derived from data or models ||| Probability of rain tomorrow based on weather forecast
• What is the likelihood of an event based on subjective probability?

  Personal judgment
• What does P(A') represent in probability notation?

  Probability of the complement of event A
• Match the notation with its meaning:

  P(A) ↔️ Probability of event A occurring

  P(A') ↔️ Probability of the complement of event A occurring
• The conditional probability of event A given that event B has occurred is denoted as $P(A \mid B)$
• Steps to calculate the probability of dependent events

  1️⃣ Calculate the probability of the first event

  2️⃣ Calculate the conditional probability of the second event

  3️⃣ Multiply the probabilities of both events
• Match the event type with its probability formula:

  Independent ↔️ $P(A \text{ and } B) =$$P(A) \times P(B)$

  Dependent ↔️ $P(A \text{ and } B) =$$P(A \mid B) \times P(B)$
• The probability formula for mutually exclusive events is $P(A \text{ or } B) =$$P(A) +$$P(B)$
• A probability of 0 indicates an impossible event.


  True
• What is the range of values for probability?

  0 to 1
• How can probability be expressed?

  Fraction, decimal, or percentage
• Empirical probability is based on observed data
• What is subjective probability based on?

  Personal judgment
• Empirical probability is calculated as the ratio of favorable outcomes to total outcomes
• Theoretical probability is based on mathematical models and calculations.


  True
• What is an example of theoretical probability?

  Probability of rolling a 6 on a fair die is 1/6
• Subjective probability is derived from data or mathematical models.

  False
• What is an example of subjective probability?

  Probability of rain tomorrow based on weather forecaster's assessment
• What is the calculation for theoretical probability?

  Total favorable outcomes / Total possible outcomes
• Theoretical probability uses mathematical models
• The value of P(A) is always between 0 and 1.


  True
• A probability of 0 means the event is impossible.


  True
• Empirical probability relies on repeated experiments.


  True
• In probability notation, P(A) denotes the probability of event A occurring.


  True
• P(A') represents the probability that event A does not occur.

  True
• An event $E$ must be a subset of the sample space S</latex>.


  True
• Favorable outcomes are the number of ways the desired event can occur.