Final answer:
The events of selecting a female economics major and selecting a 20-year-old economics major are not mutually exclusive because it is possible for an economics major to be both female and 20 years old at the same time.
Step-by-step explanation:
To determine if events A and B are mutually exclusive, we need to assess whether they can occur simultaneously. Given the examples of selecting a female economics major and selecting a 20-year-old economics major, we can infer that these two events can indeed happen at the same time. Therefore, the events are not mutually exclusive because an economics major can be both female and 20 years old at the same time.
For instance, consider option 2, which correctly states that events A and B are not mutually exclusive: No, because it is possible for a randomly selected economics major to be both female and 20 years old. This indicates the presence of overlap between the two events thus nullifying the definition of mutually exclusive events.
In a different context, if looking at events such as picking a card from a deck and flipping a coin, events would be mutually exclusive if they could not occur at the same time, such as picking a red card and a black card at the same time. In probability terms, mutually exclusive events have an intersection probability of zero: P(A AND B)=0.
Moreover, understanding the difference between independent events and mutually exclusive events is crucial in probability. Independent events have no influence on each other's occurrence, whereas mutually exclusive events cannot happen simultaneously. For example, P(musician is a female AND is self-taught) would represent two events that can be independent but not mutually exclusive if some female musicians are indeed self-taught.