U3.1 Probability

What is the primary purpose of probability in decision-making?

• To eliminate uncertainty
• To measure the likelihood of events
• To predict exact outcomes
• To provide historical data

Which of the following best describes a random experiment?

• An experiment with a predetermined outcome
• An experiment that generates well-defined outcomes
• An experiment that cannot be repeated
• An experiment with only one possible outcome

In the context of probability, what does the term 'sample space' refer to?

• The set of all possible outcomes
• The probability of an event occurring
• The average of all outcomes
• The most likely outcome

What is the complement of an event A?

• The event that A occurs
• The event that A does not occur
• The event that A and B occur
• The event that A or B occurs

Which law would you use to find the probability of either event A or event B occurring?

• Multiplication Law
• Addition Law
• Bayes' Theorem
• Conditional Probability

If two events A and B are independent, what is true about their probabilities?

• P(A and B) = P(A) + P(B)
• P(A and B) = P(A) * P(B)
• P(A | B) = P(A)
• P(A) = P(B)

What is Bayes' theorem primarily used for?

• To calculate joint probabilities
• To revise probabilities based on new information
• To find the expected value
• To determine the variance of a distribution

Which of the following distributions is used to model the number of occurrences of an event over a specified interval?

• Normal Distribution
• Binomial Distribution
• Poisson Distribution
• Exponential Distribution

What does a discrete random variable represent?

• Any numerical value
• A countable number of outcomes
• An interval of values
• A continuous range of values

What is the expected value of a random variable?

• The most frequently occurring value
• The average of all possible values weighted by their probabilities
• The highest value in the distribution
• The value that occurs with the highest probability