Question

1. If A and B are mutually exclusive events, does it follow that An and B cannot be independent events ? Give an example to demonstrate your answer. For example, discuss an election where only one person can win. Let A be the event that party A’s candidate wins, let B be the event that party B’s candidate wins. Does the outcome of one event determine the outcome of the other event ? Are A and B mutually exclusive events ?

2.Conditions under which P(A and B) = P(A) * P(B) is true. Under what conditions is this not true ?

Answer 1

Answer:

Given that:

1) If A and B are mutually exclusive events, does it follow that An and B cannot be independent events ?

Two events are mutually exclusive if they can't both happen. If A and B are mutually exclusive, knowledge that A occurred completely changes the probabilities that B may have occurred by collapsing them to 0. Events are mutually exclusive if the occurrence of one event excludes the occurrence of the other(s).

If A and B are mutually exclusive,

Independent events are events where knowledge of the probability of one doesn't change the probability of the other. If events A and B are independent, knowledge that A occurred does not change the probabilities that B may have occurred.

If A and B are independent,

In the cited election example, A and B are mutually exclusive events, because both can't simulteneously happen. Only one of the candidates can win and if A happens P(B) = 0 and vice versa. A and B can't happen indepenedently, because occurence of one event is related to the occurence of the other.

2) Conditions under which P(A and B) = P(A) * P(B) is true. Under what conditions is this not true ?

i) If A and B are independent the student

P(A and B) = P(A) * P(B) is true

ii) If A and B are not independent the student

P(A and B) = P(A) * P(B) is not true