Please explain to me why they are exclusive or not exclusive.
Event A is that atleast three of toni's five cousins are female
Event B is that atleast three of toni's five cousins are male.
These are mutually exclusive events.
http://www.mathgoodies.com/lessons/vol6/mutually_exclusive.html
Thank you..
what about a person who speaks chinese and spanish?
is that going to be mutually inclusive?
To determine whether events A and B are exclusive or not exclusive, we need to understand the relationship between them.
Event A states that at least three out of Toni's five cousins are female. This means that either exactly three, four, or all five of the cousins are female. It does not matter if the other two cousins are male or female.
Event B states that at least three out of Toni's five cousins are male. This means that either exactly three, four, or all five of the cousins are male. Again, it does not matter if the other two cousins are male or female.
Based on these definitions, events A and B can be exclusive or not exclusive depending on the actual gender distribution among Toni's cousins. Let's consider the possibilities:
If all five of Toni's cousins are female, then event A occurs (at least three cousins are female) but event B does not occur (there are no male cousins). In this case, events A and B are exclusive.
If all five of Toni's cousins are male, then event B occurs (at least three cousins are male) but event A does not occur (there are no female cousins). In this case, events A and B are also exclusive.
If exactly three or four out of Toni's cousins are female (and the remaining one or two are male), then both event A and event B occur. In this case, events A and B are not exclusive.
If exactly three or four out of Toni's cousins are male (and the remaining one or two are female), then both event A and event B occur. In this case, events A and B are also not exclusive.
So, in summary, events A and B can be exclusive (when all cousins are of the same gender) or not exclusive (when there is a mix of male and female cousins). The exclusivity depends on the actual gender distribution among Toni's five cousins.