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.
To determine whether event A and event B are exclusive or not exclusive, we need to understand the meaning of exclusivity in probability.
Exclusivity refers to two events that cannot occur simultaneously. If two events are exclusive, it means that if one event happens, the other event cannot happen at the same time. On the other hand, if two events are not exclusive, it means that they can occur simultaneously.
In this case, event A states that at least three of Toni's five cousins are female, while event B states that at least three of Toni's five cousins are male.
To determine if these events are exclusive or not, we need to consider the possibilities:
1. If all five of Toni's cousins are female, then event A occurs but event B does not, making them not exclusive.
2. If all five of Toni's cousins are male, then event B occurs but event A does not, making them not exclusive.
3. If two of Toni's cousins are female and three are male, then event A and event B both occur, making them not exclusive.
4. If three or more of Toni's cousins are female and three or more are male, then both event A and event B occur, making them not exclusive.
Based on these possibilities, we can conclude that event A and event B are not exclusive because there are scenarios in which both events can occur simultaneously.