5.1 Probability Concepts

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

  0.5
• The sample space is the set of all possible outcomes of an experiment.
• What is an event defined as in probability theory?

  Subset of sample space
• The sample space cannot be empty.


  True
• What is the formula to calculate probability using favorable outcomes and total outcomes?

  \text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}</latex>
• What is the complement rule formula?

  $P(A') =$$1 - P(A)$
• Theoretical probability is based on the ideal conditions or known sample space
• Experimental probability is calculated using the number of times an event occurs divided by the total number of trials
• Theoretical probability is calculated based on the ideal conditions or known sample space
• The theoretical probability of rolling a 3 on a fair 6-sided die is 1/6.


  True
• What is the formula for experimental probability?

  Times Event Occurs / Total Trials
• Probability is quantified as a number between 0 (impossible) and 1 (certain
• An event is a subset of the sample space.


  True
• Probability can be expressed as a fraction or a decimal
• The complement rule states that P(A') = 1 - P(A).

  True
• What is the theoretical probability of rolling a 6 on a fair 6-sided die?

  1/6
• What is probability defined as?

  Likelihood or chance
• A probability of 0 means an event is impossible.

  True
• Match the likelihood with its corresponding probability value:

  Unlikely ↔️ 0.25

  Even chance ↔️ 0.5

  Likely ↔️ 0.75

  Certain ↔️ 1
• When rolling a 6-sided die, the sample space is {1, 2, 3, 4, 5, 6}.


  True
• The sample space represents the entire possibility space
• An event can be empty if it is impossible, such as rolling a 7 on a 6-sided die.
• If there are 3 red marbles and 5 total marbles in a bag, the probability of picking a red marble is 3/5.


  True
• The probability of rolling a 4 on a 6-sided die is 1/6, which is approximately 0.167 as a decimal.
• If the probability of picking a blue marble is 3/5, the probability of not picking a blue marble is 2/5.


  True
• The theoretical probability of rolling a 3 on a fair 6-sided die is 1/6.


  True
• What is the experimental probability of rolling a 3 if it occurs 10 out of 60 times?

  1/6
• What is the formula for theoretical probability?

  Favorable Outcomes / Total Outcomes
• Experimental probability is based on the results of repeated experiments
• If you roll a die 60 times and it lands on 3 ten times, the experimental probability of rolling a 3 is 1/6.


  True
• Match the feature with the type of probability it relates to:

  Definition based on ideal conditions ↔️ Theoretical Probability

  Definition based on experimental results ↔️ Experimental Probability
• What is a sample space?

  All possible outcomes
• Match the term with its description:

  Sample Space ↔️ All possible outcomes

  Event ↔️ Subset of the sample space
• What is the formula for calculating probability as a fraction or decimal?

  Favorable Outcomes / Total Outcomes
• In the complement rule, P(A') represents the probability that event A does not occur
• If you roll a die 50 times and get a 6 seven times, the experimental probability of rolling a 6 is 7/50.

  True
• Experimental probability is affected by random variations