Question Video: Identifying the Intersection of Two Mutually Exclusive Events | Nagwa Question Video: Identifying the Intersection of Two Mutually Exclusive Events | Nagwa

Question Video: Identifying the Intersection of Two Mutually Exclusive Events Mathematics • Second Year of Secondary School

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Suppose 𝐴 and 𝐵 are mutually exclusive events. Determine P(𝐴∩𝐵).

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Video Transcript

Suppose that 𝐴 and 𝐵 are mutually exclusive events. Determine the probability of 𝐴 intersects 𝐵.

In this question, we are given two mutually exclusive events 𝐴 and 𝐵 and asked to determine the probability of 𝐴 intersects 𝐵, that is, the probability that both events occur. To answer this question, we can start by recalling that we say that two events 𝐴 and 𝐵 are mutually exclusive if they cannot both occur. In other words, the intersection of both events is the empty set.

This is enough information to answer the question. If both events 𝐴 and 𝐵 cannot happen at the same time since they are mutually exclusive, then the probability of both events occurring must be zero since it is impossible for both of them to occur. More formally, we can think of this in terms of the number of outcomes where both 𝐴 and 𝐵 occur divided by the total number of possible outcomes. Once again, we know there are no outcomes where both 𝐴 and 𝐵 occur since they are mutually exclusive. So, the probability must be zero.

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