Worked solution · Exam P
This Exam P sample reference tests Sampling Without Replacement. Favorable hands contain two, three, or four kings, no cards from the two excluded ranks, and all remaining cards from the 40 neutral cards. Summing those combinations over all five-card hands gives probability 0.02402499, so choice C is correct.
Independent solution
Setup
Partition the deck into four target cards, eight excluded cards, and forty neutral cards.
Model
Count favorable hands separately for two, three, and four target cards while choosing zero excluded cards.
Compute
Divide the favorable count by the number of unordered five-card hands.
Answer
The probability rounds to 0.0240.
Test the method on unseen problems
30 original general probability problems with complete solutions and wrong-choice analysis. Written for Exam P, not copied from the SOA set. One-time $19 PDF.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
An archive contains 6 bronze, 5 silver, and 4 gold tokens. Five tokens are selected without replacement. Given that exactly two selected tokens are bronze, calculate the probability that at least one selected token is gold.
After conditioning on two bronze tokens, the other three are drawn from five silver and four gold tokens. The probability that all three are silver is 10/84, so the probability of at least one gold is 37/42=0.880952 and choice D is correct.
Setup
Conditioning fixes two bronze selections, leaving three selections from the nine nonbronze tokens.
Model
Use the complement event that all three remaining selections are silver.
Compute
Evaluate the combination ratio.
Answer
The conditional probability rounds to 0.881.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 192 Exam P general probability practice problems.
Keep studying
Work through the related free solutions for this topic, review the formulas you used, or keep every current Exam P solution in one searchable PDF.
