Worked solution · Exam P
This Exam P sample reference tests Independence. The emergency-charge marginal is 0.75. Substituting independence into the union formula yields operating-charge probability 0.40, choice D.
Independent solution
Setup
Let E be the emergency-charge event and p the probability of an operating charge. The supplied complement gives Pr(E)=0.75.
Model
Use independence in the two-event addition rule, replacing the overlap probability by 0.75p.
Compute
Equating the union probability to 0.85 simplifies to 0.25p=0.10, hence p=0.40.
Answer
The operating-charge probability is 0.40, corresponding to choice D.
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Original practice · fully worked
Two independent diagnostic flags A and B are considered. Flag B is absent with probability 0.40, and at least one flag appears with probability 0.88. Find P(A).
Independence gives P(A absent and B absent)=0.12. Dividing by P(B absent)=0.40 gives P(A absent)=0.30, so P(A)=0.70, choice C.
Setup
Complement the at-least-one event to obtain the probability that both flags are absent.
Model
Independence makes the joint absence probability the product of the two marginal absence probabilities.
Compute
Divide 0.12 by Pr(B absent)=0.40 to get Pr(A absent)=0.30, then take the complement to obtain Pr(A)=0.70.
Answer
Flag A appears with probability 0.70, which is choice C.
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Drill the method: Exam P Independence problems
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