5.3 Conditional Probability

• P(A|B) represents the probability of event A given that event B has occurred.

  True
• Steps to solve a conditional probability problem using the formula

  1️⃣ Identify event A and event B

  2️⃣ Calculate P(A ∩ B)

  3️⃣ Calculate P(B)

  4️⃣ Apply the conditional probability formula
• What is the value of P(A|B) when drawing a red card given that a heart has already been drawn?

  $1$
• What is the relationship between P(A|B) and P(A) for independent events?

  $P(A|B) =$$P(A)$
• Drawing cards without replacement is an example of dependent events.
• The conditional probability formula is used to calculate the probability of A given that B has occurred.

  True
• What does P(A|B) represent in the conditional probability formula?

  Probability of A given B
• Conditional probability is the probability of an event A occurring regardless of event B.

  False
• The conditional probability formula allows calculating the probability of one event given another has occurred.


  True
• Match the type of event with its relationship:

  Independent Events ↔️ P(A and B) = P(A) × P(B)

  Dependent Events ↔️ P(A and B) ≠ P(A) × P(B)
• Conditional probability is the probability of an event occurring given that another event has already occurred.


  True
• For independent events, the probability of both events occurring is the product of their individual probabilities.

  True
• The probability of dependent events A and B occurring together is equal to the product of their individual probabilities.

  False
• For dependent events, the probability of A and B is not equal to the product of their individual probabilities
• When rolling a 6-sided die, the probability of rolling an odd number is 1/2.


  True
• What is conditional probability?

  Probability given another event
• What does P(A ∩ B) represent in the conditional probability formula?

  Both A and B
• What is the value of P(A ∩ B) in the example of drawing a red heart from a standard deck of 52 cards?

  $\frac{13}{52}$
• In independent events, the probability of both events occurring is the product of their individual probabilities.


  True
• Independent events affect each other's probabilities.

  False
• In dependent events, P(A ∩ B) is equal to P(A) × P(B).

  False
• What does P(A|B) mean in the conditional probability formula?

  Probability of A given B
• What does P(B) represent in the denominator of the conditional probability formula?

  Probability of event B
• What does P(B) represent in the conditional probability formula?

  Probability of event B
• What is the relationship between probabilities for independent events A and B?

  P(A and B) = P(A) × P(B)
• What is an example of an independent event?

  Flipping a coin twice
• What is the probability of drawing a red card given you have already drawn a heart from a standard deck of 52 cards?

  1
• How is the probability of two independent events calculated?

  P(A) × P(B)
• Independent events occur when the occurrence of one event does not affect the probability of the other event
• Why is drawing cards from a deck without replacement considered a dependent event?

  Composition of deck changes
• If P(A ∩ B) = 1/6 and P(B) = 1/2, then P(A|B) = 1/3
• Steps to apply the conditional probability formula

  1️⃣ Identify the two events, A and B

  2️⃣ Determine P(A ∩ B)

  3️⃣ Determine P(B)

  4️⃣ Calculate P(A|B)
• The conditional probability formula is P(A|B)
• P(B) in the conditional probability formula represents the probability of event B
• The probability of rolling an odd number with a 6-sided die is 1/2
• Steps to solve conditional probability problems using Venn diagrams

  1️⃣ Draw the Venn diagram with two circles

  2️⃣ Fill in the diagram with the given probabilities

  3️⃣ Calculate the necessary probabilities

  4️⃣ Use the conditional probability formula
• What are independent events?

  Events with no influence
• For dependent events, what is the relationship between P(A and B), P(A), and P(B)?

  P(A and B) ≠ P(A) × P(B)
• For dependent events, the probability of A and B is equal to the product of their individual probabilities.

  False
• The intersection of events A and B, P(A ∩ B), represents the probability of both events occurring together.


  True