Conditional Probability

Front

What is Conditional Probability?

Back

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

Front

How is Conditional Probability calculated?

Back

Conditional Probability is calculated using the formula: P(A|B) = P(A and B) / P(B), where P(A and B) is the probability of both events occurring and P(B) is the probability of event B.

Front

What does P(A|B) represent?

Back

P(A|B) represents the probability of event A occurring given that event B has occurred.

Front

What is the difference between independent and dependent events?

Back

Independent events are events where the occurrence of one does not affect the probability of the other. Dependent events are events where the occurrence of one event affects the probability of the other.

Front

If P(A) = 0.5 and P(B) = 0.4, what is P(A and B) if A and B are independent?

Back

If A and B are independent, P(A and B) = P(A) * P(B) = 0.5 * 0.4 = 0.2.

Front

What is the Law of Total Probability?

Back

The Law of Total Probability states that if B1, B2, ..., Bn are mutually exclusive events that cover the entire sample space, then P(A) = P(A|B1)P(B1) + P(A|B2)P(B2) + ... + P(A|Bn)P(Bn).

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

What is the probability of event A if P(A|B) = 0.3 and P(B) = 0.5?

Back

To find P(A), you need P(B|A) and P(A). Without additional information, you cannot determine P(A) directly from P(A|B) and P(B).

Front

What is an example of Conditional Probability in real life?

Back

An example of Conditional Probability is determining the probability of a student passing a test given that they studied for it. This can be expressed as P(Pass|Studied).

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 given by P(A') = 1 - P(A).