Assume that A and B are events in a probability space with the property that P(A) = 0.5, P(B) = 0.6, and P(A ∪ B) = 0.9.
1. Explain why A and B cannot be independent.
2. Is A favorable or unfavorable to B? (Remember that an event E is said to be favorable to F if P(F|E) > P(F); that is, if the knowledge that E occurred increases the plausibility of F.)
Given and .
Now
a) If A and B are independent, then. Here
Hence A and B cannot be independent.
b) We have using conditional probability
Since , A is unfavorable to B.
Assume that A and B are events in a probability space with the property that P(A)...
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