5.2 Probability Calculations

• The probability of flipping a fair coin and getting heads is 1/2.


  True
• Match the term with its definition:

  Sample Space ↔️ The set of all possible outcomes

  Event ↔️ A subset of the sample space

  Complement ↔️ All outcomes not in the event
• What is the probability formula for the intersection of independent events A and B?

  $P(A \cap B) =$$P(A) \times P(B)$
• The probability of an event is calculated as the number of favourable outcomes divided by the total number of outcomes
• Probability is a measure of the likelihood an event will occur
• When rolling a 6-sided die, the probability of rolling a 4 is 1/6
• Independent events are influenced by each other's outcomes.

  False
• What is the likelihood that an event will occur called?

  Probability
• What is the formula for calculating the probability of an event occurring?

  \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}}</latex>
• What does set theory help define in probability?

  Sample space and events
• What is the formula for the probability of the union of two events A and B?

  P(A \cup B) = P(A) + P(B) - P(A \cap B)</latex>
• If rolling a die, the probability of getting an even number (event A) is $\frac{1}{2}$ because there are 3 favourable outcomes out of 6
• What is the probability of the union of events A and B in the die-rolling example?

  \frac{2}{3}</latex>
• The sample space for rolling a die is {1, 2, 3, 4, 5, 6}.


  True
• Match the set operation with its explanation and probability formula:

  1️⃣ Union

  2️⃣ Both or one event occurring

  3️⃣ $P(A \cup B) =$$P(A) +$$P(B) - P(A \cap B)$

  4️⃣ Intersection

  5️⃣ Both events occurring

  6️⃣ $P(A \cap B)$

  7️⃣ Complement

  8️⃣ Event not occurring

  9️⃣ $P(A') =$$1 - P(A)$
• What is the probability of rolling a multiple of 3 on a die?

  $\frac{1}{3}$
• What is the probability of rolling a 4 and getting heads when flipping a coin?

  $\frac{1}{12}$
• If you draw a card from a deck and then draw a second card without replacing the first, are the events dependent or independent?

  Dependent
• What is the fundamental definition of probability?

  Likelihood of an event
• What does the term "favorable outcomes" refer to in probability calculations?

  Outcomes meeting conditions
• Set theory in probability helps define the sample space and events.

  True
• The complement of an event A is denoted as $P(A')$
• What is the sample space when rolling a die?

  $S =$$\{1, 2, 3, 4, 5, 6\}$
• What does the notation $E \subseteq S$ represent?


  Event E is a subset of S
• Match the term with its definition:

  Sample Space ↔️ All possible outcomes

  Event ↔️ A subset of the sample space

  Complement ↔️ All outcomes not in the event
• Steps to calculate probability using set theory with a die example:

  1️⃣ Define the sample space $S =$$\{1, 2, 3, 4, 5, 6\}$

  2️⃣ Define event A (even numbers) and event B (multiples of 3)

  3️⃣ Calculate $P(A)$ and $P(B)$

  4️⃣ Calculate $P(A \cap B)$

  5️⃣ Calculate $P(A \cup B)$
• Why is the probability of independent events calculated by multiplying their individual probabilities?

  Outcome of one does not influence the other
• What is the formula for the intersection of two dependent events A and B?

  $P(A \cap B) =$$P(A) \times P(B|A)$
• Drawing a card from a deck and then drawing a second card without replacement is an example of dependent events.


  True
• The formula for conditional probability is P(A|B)
• What is the condition for independent events in terms of probability?

  P(A \cap B) = P(A) \times P(B)
• Independent events occur when the outcome of one event influences the probability of another.

  False
• The probability that at least one of the two bulbs selected is defective is 0.0975.


  True
• What is a favorable outcome in probability?

  Outcome meeting the conditions
• Match the term with its definition:

  Sample Space ↔️ All possible outcomes

  Event ↔️ Subset of the sample space

  Complement ↔️ All outcomes not in the event
• The formula for calculating probability is $\frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}}$, where the numerator represents the number of favorable outcomes.
• The probability of rolling a 4 on a 6-sided die is $\frac{1}{6}$ because there is 1 favorable outcome and 6 total possible outcomes.


  True
• Match the set theory term with its LaTeX notation:

  Sample Space ↔️ S</latex>

  Event ↔️ $E \subseteq S$

  Complement ↔️ $E'$
• The probability of the complement of event A is calculated as $P(A') =$$1 - P(A)$, where $P(A)$ is the probability of event A occurring.
• When rolling a die, the sample space is $S =$$\{1, 2, 3, 4, 5, 6\}$, which includes all possible outcomes.