In the Addition Rule for disjoint events, ____________________.

Question

In the Addition Rule for disjoint events,  ____________________.

BlackTom AI · Accepted Answer

The question asks about the Addition Rule for disjoint events. In probability, the symbol 'or' typically represents the union of events A and B, written as A ∪ B.

Option considered: 'P(A or B) = P(A) + P(B).' This statement is true when A and B are disjoint (mutually exclusive), meaning A ∩ B = ∅. In that case, the probability of A or B occurring is simply the sum of their individual probabilities, since the events cannot happen at the same time to double-count.

Delving into the general rule helps: P(A ∪ B) = P(A) + P(B) − P(A ∩ B). This formula works for any events A and B. When A and B are disjoint, P(A ∩ B) = 0, so the formula reduces to P(A ∪ B) = P(A) + P(B). Therefore, the given statement aligns with the disjoint-events case.

It is worth contrasting with non-disjoint scenarios: if A and B are not disjoint, simply adding P(A) and P(B) would double-count the outcomes that lie in both A and B. In those cases the correction term P(A ∩ B) must be subtracted.

There are no alternative options provided in the list to evaluate here, but the core idea remains: for disjoint events, the addition rule collapses to the sum of the individual probabilities since there is no overlap to subtract.

STAT 1450.02 SP2025 (28132) Checkpoint 12.3 & 12.4

In the Addition Rule for disjoint events, ____________________.

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