This one has me really confused.
We know that A and B are mutually exclusive – so there’s zero overlap.
And we know that both events happening at the same time = A x B.
Since there is zero overlap, both events can’t happen at the same time, so shouldn’t A x B = 0?
Please help me understand how to go about this one? and where is my understanding wrong?
Great question.
You’re mistaking a probability rule for a logic rule.
A and B can not happen at the same time
But that does not mean A x B = 0
A = probability it rains tomorrow
B = probability it does not rain tomorrow
Since one and only one of these must happen, A + B = 1
And we are being asked: what is the maximum value of A × B?
This is not about mutually exclusive events both happening.
Instead, we’re looking for the maximum possible value of A x B, under the constraint A + B = 1.
and we can get the max value of A x B when both A and B are super close to each other in the middle. So A = 0.5 and B = 0.5, and A x B = 0.25?
Please correct me here if I’m wrong
Exactly
