This Exam P sample reference tests Binomial Distribution. A payment of 60 supports two awards; the probability of at least three successes is 0.00707. Any larger listed payment fails already at two successes, so choice D.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AA payment of 24 is smaller and therefore also satisfies the reserve constraint, but it is not the largest listed feasible payment.
BA payment of 30 is feasible but smaller than the feasible amount 60, so it does not maximize the requested payment.
CA payment of 40 is also feasible, but 60 remains feasible and is larger.
EA payment of 120 allows only one award before shortfall. The probability of at least two awards is 0.059899, which exceeds 0.01.
Original practice · fully worked
Original variant: capacity probability for rare independent awards
Twelve independent grant applications each have probability 0.05 of receiving an award. A reserve can fund at most two awards. Find the probability that the reserve is adequate.
A 0.88164
B 0.95000
C 0.98043
D 0.98460
E 0.99900
Variant answer in brief
The award count is binomial, and adequacy means at most two awards. The cumulative probability is 0.98043, choice C.
Setup
Setup
Let X count awards among the 12 independent applications; then X is binomial with success probability 0.05.
X∼Bin(12,0.05)
Model
Model
The reserve is adequate exactly when at most two awards occur, so sum the binomial masses for counts zero, one, and two.
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