Consider two events A and B in the same sample space such that P(A)=0.4 and P(B)=0.3. Then A and B are mutually exclusive.

question: Is it true or false?

Not necessarily true.

To determine whether events A and B are mutually exclusive, we need to check if they can both occur at the same time or not.

Mutually exclusive events are events that cannot occur simultaneously. In other words, if event A happens, then event B cannot happen, and vice versa.

To understand if A and B are mutually exclusive, we need to look at their probabilities. If P(A) + P(B) equals 1 or more, then A and B are not mutually exclusive. However, if P(A) + P(B) is less than 1, then A and B are mutually exclusive.

Let's calculate P(A) + P(B) and compare it to 1:

P(A) + P(B) = 0.4 + 0.3 = 0.7

Since 0.7 is less than 1, we can conclude that A and B are mutually exclusive.