5.2 Probability Calculations

• A probability of 0.5 means an event is equally likely to happen or not happen.


  True
• A sample space is the set of all possible outcomes
• What is the size of the sample space for flipping a coin twice?

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

  1/6
• How many unique cards are in a standard deck?

  52
• What is the probability of flipping a coin and getting heads?

  1/2
• The set of all possible outcomes for an experiment is called the sample space.
• What is the probability of rolling a 3 on a 6-sided die?

  1/6
• Independent events are events where the outcome of one affects the probability of the other.

  False
• Match the type of event with its characteristic:

  Independent Events ↔️ Outcome of one event does not affect the other

  Dependent Events ↔️ Outcome of one event affects the other
• To calculate the probability of two independent events A and B occurring together, you use the formula P(A and B) = P(A) × P(B).
• Probability is a measure of how likely an event is to occur
• What is the probability of rolling a 7 on a standard six-sided die?

  0
• Match the experiment with its sample space:

  Rolling a 6-sided die ↔️ {1, 2, 3, 4, 5, 6}

  Flipping a coin ↔️ {Heads, Tails}

  Drawing a card from a standard deck ↔️ {52 cards}
• Steps to calculate simple probabilities:

  1️⃣ Identify the sample space

  2️⃣ Identify the event

  3️⃣ Calculate the probability
• A probability of 0 means an event is certain to happen.

  False
• The sample space is crucial for calculating probabilities accurately
• What are the steps to calculate simple probabilities?

  Identify sample space, event, probability
• The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

  True
• When rolling a 6-sided die, the sample space is {1, 2, 3, 4, 5, 6}.
• Give an example of two independent events.

  Rolling a die and flipping a coin
• The probabilities of independent events can be multiplied to find the probability of both events occurring together.

  True
• What is the probability of rolling a 3 on a die (1/6) and flipping heads on a coin (1/2)?

  1/12
• What is the probability of rolling a 4 on a 6-sided die and flipping heads on a coin?

  1/12
• The formula for calculating the probability of mutually exclusive events A or B is P(A or B) = P(A) + P(B).
• Mutually exclusive events cannot occur together, while non-mutually exclusive events can occur together.


  True
• Mutually exclusive events cannot occur together
• What is the addition rule for mutually exclusive events?

  $P(A \text{ or } B) =$$P(A) +$$P(B)$
• What is the addition rule for non-mutually exclusive events?

  $P(A \text{ or } B) =$$P(A) +$$P(B) - P(A \text{ and } B)$
• The probability of rolling an even number on a 6-sided die is 1/2
• Probability is expressed as a number between 0 and 1
• Match the experiment with its sample space size:

  Rolling a 6-sided die ↔️ 6

  Flipping a coin ↔️ 2

  Drawing a card from a standard deck ↔️ 52
• The probability of rolling an even number on a 6-sided die is 1/2
• What is the sample space when rolling a standard die?

  {1, 2, 3, 4, 5, 6}
• Independent events affect each other's outcomes.

  False
• The probability of two independent events A and B occurring together is P(A) × P(B)
• Rolling a die and flipping a coin are examples of independent events.


  True
• To calculate the probability of two independent events occurring together, you multiply their individual probabilities
• Dependent events are affected by the outcome of previous events.


  True
• Drawing a card from a deck with replacement is an example of dependent events.

  False