Worked solution · Exam P
This Exam P sample reference tests Binomial Distribution. The affected-applicant count is Binomial(200,0.01). Summing its masses from zero through five gives 0.9839770931, which rounds to 0.98 and choice E.
Independent solution
Setup
Let X count affected applicants in the independent sample.
Model
The requested lower tail contains the six disjoint counts from zero through five.
Compute
Evaluate the finite binomial sum without rounding its terms prematurely.
Answer
The probability rounds to 0.98.
Test the method on unseen problems
30 original univariate random variables problems with complete solutions and wrong-choice analysis. Written for Exam P, not copied from the SOA set. One-time $19 PDF.
Error diagnosis
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Original practice · fully worked
A gateway monitors four legacy sensors and six upgraded sensors. During a diagnostic window, each legacy sensor independently flags with probability 0.30 and each upgraded sensor independently flags with probability 0.10. All ten flag events are independent. Calculate the probability that at most one sensor flags.
No flags has probability 0.7⁴ times 0.9⁶. Exactly one flag can come from either sensor generation. Adding those three disjoint contributions gives 0.4314060891, so choice E.
Setup
Separate the zero-flag event from the two ways to receive exactly one flag.
Model
For exactly one flag, either one legacy sensor flags or one upgraded sensor flags.
Compute
Add the mutually exclusive count cases.
Answer
The probability of at most one flag rounds to 0.4314.
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