Probability of Union of Two Events

Probability of Union of Two Events

Intersection of Events

• The intersection of two events A and B, denoted as A ∩ B, represents the occurrence of both events.
• The probability of the intersection of two events is denoted as P(A ∩ B).
• The probability of the intersection of two events can be calculated using the formula:

P(A ∩ B) = P(A) × P(B|A) = P(B) × P(A|B)

Where P(A|B) is the conditional probability of event A given event B, and P(B|A) is the conditional probability of event B given event A.

Independent Events

• Two events A and B are said to be independent if the occurrence of one event does not affect the probability of the other event.
• If A and B are independent, then:

P(A ∩ B) = P(A) × P(B)

• In other words, the probability of the intersection of two independent events is the product of their individual probabilities.

Mutually Exclusive Events

• Two events A and B are said to be mutually exclusive if they cannot occur simultaneously.
• If A and B are mutually exclusive, then:

P(A ∩ B) = 0

• In other words, the probability of the intersection of two mutually exclusive events is zero.

Probability of Union of Two Events

• The probability of the union of two events A and B, denoted as A ∪ B, represents the occurrence of at least one of the events.
• The probability of the union of two events can be calculated using the formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

• Note that if A and B are mutually exclusive, then P(A ∩ B) = 0, and the formula simplifies to:

P(A ∪ B) = P(A) + P(B)