This Exam P sample reference tests Inclusion–Exclusion. The union has probability 0.65, and the two-event addition rule leaves intersection probability 0.05, which is choice A.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
EThe value 0.35 is the supplied probability of neither event, not the intersection. Its complement is used to obtain the union.
Original practice · fully worked
Original variant: combine a conditional overlap with two marginals
A learning platform records that 52% of users open a lesson and 47% open a practice set. Among practice-set users, 60% also open a lesson. Determine the probability that a user opens at least one of the two resources.
A 0.520
B 0.708
C 0.718
D 0.752
E 0.990
Variant answer in brief
The conditional rate makes the overlap 0.282. Subtracting that overlap from the marginal sum gives union probability 0.708, choice B.
Setup
Setup
Let L be the event that a lesson is opened and P the event that a practice set is opened. Convert the conditional percentage into their joint probability.
Pr(L∩P)=Pr(L∣P)Pr(P)=0.60(0.47)=0.282
Model
Model
The probability of at least one resource is the union, so apply the addition rule and subtract the overlap once.
Pr(L∪P)=Pr(L)+Pr(P)−Pr(L∩P)
Compute
Compute
The overlap is 0.60(0.47)=0.282; substituting it into the union formula gives 0.708.
Pr(L∪P)=0.52+0.47−0.282=0.708
Answer
Answer
Therefore the probability of opening at least one resource is 0.708, which is choice B.
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