Worked solution · Exam P
This Exam P sample reference tests Hypergeometric Distribution. The inventory contains 10 defective and 70 sound modems. A hypergeometric calculation for two defectives in five gives about 0.102, choice C.
Independent solution
Setup
Combine the two inventory groups to obtain 10 defective and 70 sound modems among 80 total.
Model
For a sample of five without replacement, choose two items from the 10 defectives and three from the 70 sound items, then divide by all five-item samples.
Compute
The hypergeometric combination ratio evaluates to 0.10177.
Answer
The probability rounds to 0.102, corresponding to choice C.
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Original practice · fully worked
A crate contains 12 high-capacity and 48 standard batteries. Six batteries are sampled without replacement. Find the probability exactly two sampled batteries are high-capacity.
The hypergeometric ratio C(12,2)C(48,4)/C(60,6) gives the required probability.
Setup
The crate contains 12 high-capacity and 48 standard batteries, and six are selected without replacement.
Model
Count samples with exactly two high-capacity batteries by choosing two of 12 and four of 48, then divide by all six-battery samples.
Compute
The resulting hypergeometric combination ratio is 0.256518.
Answer
The exact-two probability is 0.2565, corresponding to choice A.
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