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Answer in Statistics and Probability for Bob #86661

Author:
January 24th, 2023

Multiplication rule for two independent events:

When A and B are two independent events, then the combined probability of A and B is given by

“P(A cap B)=P(A)*P(B)”“P(A cap B)=0.2*0.5=0.1, True”

For any two events A and B, the probability that either A or B will occur is given by the inclusion-exclusion rule 

“P(A cup B)=P(A)+P(B)-P(A cap B)”“P(A cup B)=0.2+0.5-0.1=0.6, True”

The conditional probability of A given B is 

“P(A|B)=P(A cap B)/P(B)”

Event A is independent of B if the conditional probability of A given B is the same as the unconditional probability of A. That is, they are independent if 

“P(A|B)=P(A)”“0.2=0.2, True”

Therefore, all three statements are true: (|) and (II) and (III).

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