2.6 Probability

• Probability can be expressed as a fraction, decimal, or percentage
• Match the probability value with its meaning:

  0 ↔️ Impossible

  0.5 ↔️ Equally likely

  1 ↔️ Certain
• Theoretical probability is calculated based on possible outcomes
• What are the three ways to express probability?

  Fraction, decimal, percentage
• What is the decimal equivalent of flipping a fair coin and landing on heads?

  0.5
• How is experimental probability calculated?

  Event occurrences / Total trials
• What is experimental probability based on?

  Observed outcomes from experiments
• Experimental probability is calculated from all possible outcomes

  False
• What is the experimental probability of getting heads if a coin lands on heads 23 times out of 50 flips?

  0.46
• What is probability a measure of?

  Likelihood of an event
• The range of probability goes from 0 to 1.


  True
• What is experimental probability based on?

  Observed outcomes
• If heads appears 23 times out of 50 coin tosses, the experimental probability of heads is 0.46.

  True
• A fraction represents the ratio of favorable outcomes to total possible outcomes
• The range of probability goes from 0 to 1.


  True
• Theoretical probability is calculated by dividing favorable outcomes by total possible outcomes
• Theoretical probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes
• Match the type of probability with its calculation:

  Experimental Probability ↔️ Number of times event occurs / Total number of trials

  Theoretical Probability ↔️ Number of favorable outcomes / Total number of possible outcomes
• Probability can be expressed as a fraction, decimal, or percentage
• Fractions, decimals, and percentages are different ways to represent the same likelihood of an event

  True
• What is the sample space when rolling a fair 6-sided die?

  {1, 2, 3, 4, 5, 6}
• What is the probability of rolling a 4 on a fair die expressed as a fraction?

  1/6
• Steps to calculate probability using the sample space:

  1️⃣ Identify the sample space

  2️⃣ Determine the number of favorable outcomes

  3️⃣ Divide the number of favorable outcomes by the total number of possible outcomes
• The theoretical probability of rolling a 4 on a fair die is 1/6
• What is the complementary probability of an event that has a probability of 0.7?

  0.3
• What is the formula for calculating the probability of two independent events A and B occurring together?

  P(A and B) = P(A) × P(B)
• Mutually exclusive events can happen together in the same trial

  False
• The range of probability goes from 0 (impossible event) to 1 (certain event
• What are mutually exclusive events?

  Events that cannot happen together
• Probability ranges from -1 to 1.

  False
• Match the probability range with its meaning:

  0 ↔️ Impossible

  0.5 ↔️ Equally likely

  1 ↔️ Certain
• Experimental probability is calculated based on theoretical outcomes.

  False
• Theoretical probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes
• What is the theoretical probability of getting heads on a fair coin flip?

  0.5
• In a bag with 2 green balls and 8 red balls, the probability of drawing a green ball as a fraction is 1/5
• Steps to calculate probability using the sample space:

  1️⃣ Identify the sample space

  2️⃣ Determine the total number of possible outcomes

  3️⃣ Determine the number of favorable outcomes

  4️⃣ Divide the number of favorable outcomes by the total number of possible outcomes
• The sample space includes all possible outcomes
• The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes
• Steps to calculate probability using the sample space

  1️⃣ Identify the sample space and the total number of possible outcomes

  2️⃣ Determine the number of favorable outcomes

  3️⃣ Divide the number of favorable outcomes by the total number of possible outcomes
• What is the formula for complementary probability?

  P(\text{Not Event}) = 1 - P(\text{Event})</latex>