Chapter 5 MCQ Review

Front

What is the probability of an event?

Back

The probability of an event is a measure of the likelihood that the event will occur, expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

Front

Define conditional probability.

Back

Conditional probability is the probability of an event occurring given that another event has already occurred, denoted as P(A|B).

Front

What is the formula for calculating conditional probability?

Back

P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of both events A and B occurring.

Front

Explain the concept of independent events.

Back

Two events are independent if the occurrence of one does not affect the probability of the other occurring. For independent events A and B, P(A ∩ B) = P(A) * P(B).

Front

What is the complement of an event?

Back

The complement of an event A, denoted as A', is the event that A does not occur. The probability of the complement is P(A') = 1 - P(A).

Front

How do you calculate the probability of the union of two events?

Back

The probability of the union of two events A and B is given by P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Front

What is Bayes' theorem?

Back

Bayes' theorem relates the conditional and marginal probabilities of random events. It is expressed as P(A|B) = [P(B|A) * P(A)] / P(B).

Front

Define a random variable.

Back

A random variable is a variable that takes on numerical values determined by the outcome of a random phenomenon.

Front

What is the difference between discrete and continuous random variables?

Back

Discrete random variables take on a countable number of distinct values, while continuous random variables can take on any value within a given range.

Front

What is a probability distribution?

Back

A probability distribution describes how the probabilities are distributed over the values of the random variable.