The probability model has a sample space of {A,B,C} with P(A) = 0.1, P(B) = 0.8, P(C) = 0.1. I found that P(B or C) = 0.9 because the probabilities add, but I cannot figure out P(A and B).
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$\begingroup$Think about what this means:
$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$
I suggest drawing a Venn Diagram to see what the quantities in this formula represent. You'll find that one of the quantities must be zero.
If the events are disjoint $P(A \cap B)=0$.
$\endgroup$ $\begingroup$Think about what this means:
P(B or C)=P(B)+P(C)−P(B and C) P(B)=0.8 P(C)=0.1 P(B or C)=0.9 so, we got P(B and C)=0 i.e.P(B ∩ C)=0 that denotes both B and C are disjoint events.
Similarly, P(A or B)=P(A)+P(B)−P(A and B) P(A) = 0.1, P(B) = 0.8 P(A and B)=P(A)+P(B)-P(A or B) P(A and B)=0.9-P(A or B) P(A and B) will be minimum when both are disjoint, i.e. 0 P(A and B) will be maximum when one is subset of other i.e. 0.1 0<=P(A ∩ B)<=0.1
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