One student is selected at random from a student body. Suppose the probability that this student is female is 0.5 and the probability that this student works part time is 0.6. Are the two events "female" and "working" mutually exclusive?
Think of it, mutually exclusive would mean that females cannot work. What do you think?
No
To determine whether the two events "female" and "working" are mutually exclusive, we need to consider if they can both occur at the same time.
Events are considered mutually exclusive if they cannot happen simultaneously. In this case, if the probability of being female and the probability of working part-time are both positive, it means that there could be individuals who fall into both categories.
Given that the probability of someone being female is 0.5 and the probability of someone working part-time is 0.6, it implies that there is a non-zero chance of a student being both female and working part-time.
Therefore, the two events "female" and "working" are not mutually exclusive.