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.
In order to determine whether events A and B are exclusive or not exclusive, we need to understand what the events are implying.
Event A states that at least three of Toni's five cousins are female. This means that there can be three, four, or all five of Toni's cousins who are female.
Event B states that at least three of Toni's five cousins are male. Similarly, this means that there can be three, four, or all five of Toni's cousins who are male.
To check if the events are exclusive (cannot occur at the same time) or not exclusive (can occur at the same time), we need to compare the possibilities.
If Toni has three female cousins and three male cousins, both events A and B can occur at the same time since the requirements for both are met. This means that the events are not exclusive, as they can coexist.
However, if Toni has four or five female cousins, it is not possible for event B to occur, because there are not enough male cousins to meet the requirement. In this case, event A would be possible, but event B would not. Therefore, in these scenarios, the events are exclusive.
In summary, events A and B are exclusive when Toni has more than three female cousins, but they are not exclusive when Toni has exactly three female cousins and three male cousins.