Worked solution · Exam P
This Exam P sample reference tests Hypergeometric Distribution. Choose one of two items in the first category, two of four in the second, and three of seven in the third. Dividing the resulting 420 favorable subsets by C(13,6)=1716 gives 0.24476, choice D.
Independent solution
Setup
Use an unordered six-item sample because all subsets of six claims are equally likely.
Model
Choose the required number independently within each claim category.
Compute
Evaluate the favorable count and divide by the common sample-space count.
Answer
The probability rounds to 0.245.
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Original practice · fully worked
A cabinet contains three red cartridges, four blue cartridges, and five green cartridges. Four cartridges are sampled without replacement. What proportion of such samples contain cartridges in just two colors?
Count four-subsets within each color pair and remove monochromatic subsets. The three pair contributions are 34, 65, and 120, so 219 of 495 samples contain exactly two colors, giving 0.4424, choice B.
Setup
Count all four-cartridge subsets.
Model
For each pair of colors, count subsets drawn from that pair and exclude one-color subsets.
Compute
Add the disjoint exact-two-color counts and divide by all samples.
Answer
Exactly two colors are represented with probability about 0.4424.
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