2.6 Probability

• What is the definition of probability?

  Likelihood of an event
• Match the type of probability event with its definition:

  Independent Events ↔️ One event does not affect another

  Dependent Events ↔️ One event influences another

  Mutually Exclusive Events ↔️ Cannot occur simultaneously
• Probability can be expressed as a fraction, decimal, or percentage
• Mutually exclusive events cannot occur at the same time
• A frequency table lists the number of times each event occurs.
• To calculate probability from frequencies, we use a **frequency table
• Arrange the probabilities of rolling each outcome in descending order based on the frequencies provided.

  1️⃣ Rolling a 2 (1/5)

  2️⃣ Rolling a 1 or 6 (1/6)

  3️⃣ Rolling a 4 (11/60)

  4️⃣ Rolling a 5 (3/20)

  5️⃣ Rolling a 3 (2/15)
• What is the Multiplication Rule for independent events A and B?

  $P(A) \times P(B)$
• Match the type of probability event with its example:

  Independent Events ↔️ Rolling a die and flipping a coin

  Dependent Events ↔️ Drawing a card without replacement

  Mutually Exclusive Events ↔️ Rolling a 3 or a 6 on a die
• The probability of an event is always calculated by dividing its frequency by the total number of events.

  True
• Empirical probabilities are useful when theoretical probabilities are unknown or difficult to calculate.


  True
• What is the Multiplication Rule used to calculate for independent events?

  The probability of both occurring
• The Addition Rule is applicable only to events that are mutually exclusive
• What is the key difference between dependent and independent events?

  Outcome affects probabilities
• What is the formula for calculating probability in general?

  \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}</latex>
• The outcome of one event does not affect the outcome of another in independent events.
• The formula to calculate probability from frequencies is Frequency of event divided by the total number of events.
• What is the probability of flipping a coin twice and getting heads both times?

  1/4
• What is the probability of rolling a 3 or a 4 on a standard 6-sided die?

  1/3
• What is the probability of rolling a 6 on a die and flipping a coin to get heads?

  1/12
• What are independent events?

  Outcome of one does not affect another
• Drawing a card from a deck without replacement is an example of a dependent event.

  True
• The probability of a student preferring football in a survey of 100 is 0.3.


  True
• A probability of 0.25 (25%) means the event has a relatively low likelihood
• To calculate probability, use the formula: Probability = Number of favorable outcomes / Total number of possible outcomes
• The formula for calculating probability is: Probability = Number of favorable outcomes / Total number of possible outcomes.


  True
• The probability of an impossible event is 0.

  True
• What is an example of an independent event?

  Rolling a die
• What is the formula for calculating probability from frequencies?

  Frequency of event / Total number of events
• What is the formula for calculating probability from frequencies?

  $\frac{\text{Frequency of event}}{\text{Total number of events}}$
• The probability of rolling a 1 on a 6-sided die after 60 rolls is 1/6.


  True
• The Addition Rule for mutually exclusive events A and B states that \( P(A \text{ or } B) = P(A) + P(B)
• What is the formula for calculating probability using favorable and total outcomes?

  $\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$
• Rolling a 3 or a 6 on a standard die are examples of mutually exclusive events
• What is the formula for calculating probability from frequencies?

  $\text{Probability} =$$\frac{\text{Frequency of event}}{\text{Total number of events}}$
• The Addition Rule states that for mutually exclusive events A and B, \( P(A \text{ or } B) = P(A) + P(B) \). In the example of rolling a die, \( P(3 \text{ or } 4) = \frac{1}{3} \), which demonstrates the combined
• Steps to apply the Addition Rule for probabilities

  1️⃣ Identify mutually exclusive events A and B

  2️⃣ Calculate the individual probabilities P(A) and P(B)

  3️⃣ Add the probabilities: P(A or B) = P(A) + P(B)
• Rolling a die and flipping a coin are examples of independent events.


  True
• Probability can be expressed as a fraction, decimal, or percentage.


  True
• Match the type of probability event with its explanation:

  Independent Events ↔️ One event does not affect another

  Dependent Events ↔️ One event influences another

  Mutually Exclusive Events ↔️ Two events cannot occur together