The probability that both events A and B occur is denoted by which expression?

The probability that both events A and B occur is denoted by which expression?

• A. P[A] + P[B]
• B. P[A ∩ B]
• C. P[A or B]
• D. P[A ∪ B]

Answer: (B)

The expression for the probability that both events occur is the intersection of A and B. This is written as P[A ∩ B], and it corresponds to the overlap region in a Venn diagram where both conditions are true. It represents the joint likelihood of A and B happening together. Adding the probabilities P[A] and P[B] would overcount the outcomes where both occur (unless A and B are mutually exclusive, which they generally are not). The probability of at least one of the events happening is P[A ∪ B], which is computed as P[A] + P[B] − P[A ∩ B].

The expression for the probability that both events occur is the intersection of A and B. This is written as P[A ∩ B], and it corresponds to the overlap region in a Venn diagram where both conditions are true. It represents the joint likelihood of A and B happening together.

Adding the probabilities P[A] and P[B] would overcount the outcomes where both occur (unless A and B are mutually exclusive, which they generally are not). The probability of at least one of the events happening is P[A ∪ B], which is computed as P[A] + P[B] − P[A ∩ B].