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
Answer and calculation
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.
0.708(B) 