5.3 Conditional Probability

• Conditional probability is denoted as P(A|B)
• Independent events are events where the occurrence of one event affects the probability of the other event.

  False
• What is the formula for conditional probability?

  P(A|B) = \frac{P(A \cap B)}{P(B)}</latex>
• The event A and B together in rolling a die is rolling a 4
• What is the probability of rolling a number greater than 3 on a fair six-sided die?

  1/2
• Steps to calculate conditional probability using the formula

  1️⃣ Identify events A and B

  2️⃣ Calculate P(A and B)

  3️⃣ Calculate P(B)

  4️⃣ Apply the formula to find P(A|B)
• For independent events, P(A and B) = P(A) × P(B)
• Conditional probability is denoted as P(A|B)
• What is the probability of two independent events A and B occurring together?

  P(A) × P(B)
• Conditional probability is denoted as P(A|B)
• What is the formula for conditional probability?

  P(A|B) = \frac{P(A \text{ and } B)}{P(B)}</latex>
• P(A|B) is the probability of event A occurring given that event B has already occurred.
• What is the probability of rolling an even number and a number greater than 3 on a fair six-sided die?

  1/3
• The probability of event B occurring on a fair six-sided die is 1/2
• How do you calculate the probability of rolling an even number on a fair six-sided die given that you rolled a number greater than 3?

  P(A|B) = 2/3
• Steps to calculate conditional probability using the formula P(A|B) = P(A and B) / P(B)

  1️⃣ Identify events A and B

  2️⃣ Calculate P(A and B)

  3️⃣ Calculate P(B)

  4️⃣ Apply the formula to find P(A|B)
• Match the real-world scenario with its application of conditional probability:

  Weather Forecasting ↔️ P(Rain | High Humidity)

  Medical Diagnosis ↔️ P(Disease | Symptoms)

  Marketing Strategies ↔️ P(Purchase | Customer Demographics)
• What is the probability of rolling an even number on a fair six-sided die given that you rolled a number greater than 3?

  2/3
• The probability of both events A and B occurring together in the example is 1/3
• In conditional probability, the occurrence of event B affects the probability of event A.
• What are some real-world scenarios where conditional probability is used?

  Weather, medicine, marketing
• To solve conditional probability problems, you first identify events A and B.
• Conditional probability helps determine the likelihood of a disease given certain symptoms
• Conditional probability is used in weather forecasting to predict rain given high humidity.
• Match the application of conditional probability with its purpose:

  Medical Diagnosis ↔️ Diagnose diseases more accurately

  Marketing Strategies ↔️ Target marketing campaigns effectively
• The formula for conditional probability is P(A|B)
• Calculating P(A and B) involves finding the probability of both A and B occurring together.
• In the example, the probability of drawing a red ball given that you drew a ball that is not blue is 1.
• Conditional probability is the probability of an event A occurring, given that event B has already occurred
• The conditional probability formula is P(A|B) = \frac{P(A \text{ and } B)}{P(B)}</latex>.
• Steps to solve conditional probability problems:

  1️⃣ Identify events A and B

  2️⃣ Calculate P(A and B)

  3️⃣ Calculate P(B)

  4️⃣ Apply the conditional probability formula
• For independent events, P(A and B) is calculated as P(A) * P(B).
• The probability of A and B for independent events is the product of their individual probabilities
• The probability of rolling an even number on a six-sided die, given that the number rolled is greater than 3, is 2/3.