| Course | HS345 Biostatistics |
|---|---|
| Unit | Unit 4 |
| Paper type | Probability problem set |
| Length | About 850 words, 6 pages double-spaced |
| Format | APA 7 student paper |
| School | Purdue University Global |
| Program | BS in Health Science |
| Updated | October 2026 |
Free sample paper for HS345 Unit 4
How Often Would This Happen Anyway? A Unit 4 Probability Problem Set From Readmissions to a Twenty-Indicator Dashboard
[Student Name]
Purdue University Global
HS345: Biostatistics
Unit 4 Probability Problem Set
[Instructor Name]
[Date]
The discharges, procedures and dashboard are composite; the blood type shares are approximate published US figures, and the statistics sources cited are real.
How Each Problem Is Laid Out
Every problem uses the same four parts: the scenario, the probability rule that applies, the work, and what the answer means for the person who asked. The rules are the ones the unit covers: conditional probability from a table, the multiplication rule for independent events, the complement rule and the binomial distribution (Pagano et al., 2022).
Problem 1: Readmission by Discharge Destination
Scenario: [1,200] composite discharges in one quarter, [1,020] to home and [180] to a skilled nursing facility. Within 30 days, [97] home discharges and [35] skilled nursing discharges were readmitted.
Rule: a probability from a table is a count over its total; a conditional probability restricts the total to one row.
Work: overall readmission, 132 of 1,200, or 11.0 percent. Given discharge home, 97 of 1,020, or 9.5 percent. Given discharge to skilled nursing, 35 of 180, or 19.4 percent.
Meaning: patients sent to skilled nursing were readmitted about twice as often. That does not show the facilities caused readmissions, since sicker patients are more likely to be discharged there.
Problem 2: Donors for a B-Negative Patient
Scenario: a patient with B-negative blood can receive B-negative or O-negative red cells. Approximate US shares are about 1.5 percent B-negative and 6.6 percent O-negative.
Rule: for mutually exclusive outcomes, add; for independent donors, multiply; for "none," use the complement.
Work: a random donor is compatible with probability 0.015 plus 0.066, or 0.081. The chance that none of ten random donors is compatible is 0.919 raised to the tenth power, or about 0.43.
Meaning: a drive that draws ten random donors will fail to find even one compatible donor for this patient about 43 percent of the time, which is why blood services recruit by type.
Problem 3: Four Surgical Site Infections in 60 Procedures
Scenario: a unit's long-run infection rate for a procedure is 2 percent. Last quarter, 4 of 60 procedures were followed by infection.
Rule: the binomial distribution, which applies when each of a set number of procedures carries the same chance of infection and one case does not affect another.
Work: with n of 60 and p of 0.02, the probabilities of 0, 1, 2 and 3 infections are about 0.298, 0.364, 0.219 and 0.087, summing to about 0.968. The chance of 4 or more is about 0.032.
If nothing had changed, a quarter this bad would happen about once every eight years, rare enough to justify a review but not rare enough to prove a lapse.
Meaning: the result supports looking at the four cases for a common factor. It does not establish that anything went wrong, and the review should say so.
Problem 4: A Positive Screening Result
Scenario: a cholesterol condition affects 1 in 250 people. A screening test detects 95 percent of true cases and wrongly flags 2 percent of people without the condition.
Rule: conditional probability, applied with a table of 100,000 people.
Work: 400 have the condition; 380 test positive. Of 99,600 without it, 1,992 test positive. Of 2,372 positives, 380 have the condition, or 16.0 percent.
Meaning: a positive screen means about a one in six chance of the condition, so a confirmatory test is needed before anyone is labeled. The other five in six are healthy people who will worry, return for testing and perhaps be offered medicine they do not need, which is the hidden cost of screening a large population for a rare condition.
Problem 5: The Dashboard With Twenty Indicators
Scenario: a quality dashboard tracks twenty independent indicators, each flagged red when it crosses a limit that a stable process crosses 5 percent of the time.
Rule: complement and multiplication rules.
Work: the chance that no indicator flags in a month is 0.95 raised to the twentieth power, or about 0.36. The chance at least one flags is about 0.64.
Meaning: in roughly two months out of three, at least one red flag will appear even if every process is stable. A red indicator is a reason to look, not evidence of a problem by itself.
What the Five Problems Share
Each answer replaced an impression with a number. Twice the number confirmed the concern, in readmissions after skilled nursing and in the infection cluster, though neither proved a cause. Twice it deflated the concern, in the screening result and the dashboard. Once it explained a practical problem, the donor search. Asking how often something would happen by chance before reacting is the habit the unit is meant to build (Bland, 2015). None of these probabilities is the chance that a concern is true; each is the chance of the data if nothing unusual were happening, a distinction often blurred in reports (Wasserstein & Lazar, 2016).
References
Bland, M. (2015). An introduction to medical statistics (4th ed.). Oxford University Press.
Pagano, M., Gauvreau, K., & Mattie, H. (2022). Principles of biostatistics (3rd ed.). CRC Press.
Wasserstein, R. L., & Lazar, N. A. (2016). The ASA statement on p-values: Context, process, and purpose. The American Statistician, 70(2), 129-133. https://doi.org/10.1080/00031305.2016.1154108
HS345 Unit 4 instructions, in plain terms
Unit 4 typically gives several short applied problems requiring the complement rule, the multiplication rule, conditional probability from a table and the binomial distribution. Sets usually span three or four pages. Marks follow correct use of each rule, work shown clearly enough to award partial credit, and an interpretation that says what the probability means for the person in the scenario. Many sections reward stating assumptions, such as independence, and noting when they may not hold. Software is often allowed if inputs are shown. A consistent layout for every problem makes the set easier to grade, and a short closing paragraph tying the problems together often earns extra credit.
Inside the HS345 Unit 4 example
An opening paragraph explains the four-part layout and lists the rules the unit covers. Problem 1 computes overall and conditional readmission probabilities from a two-way table and warns against causal reading. Problem 2 adds two blood type shares and raises the complement to the tenth power. Problem 3 sums binomial probabilities for zero to three infections; the highlighted sentence converts the result into a frequency in years. Problem 4 builds a table of one hundred thousand people to find the predictive value of a positive screen and its hidden cost. Problem 5 applies the complement rule to twenty indicators. A closing section sorts the five results and distinguishes the probability of data from the probability that a concern is true.
Where the points sit in the HS345 Unit 4 rubric
Problem sets in this unit are scored mostly on correct application of probability rules and on meaningful interpretation. Rule application covers choosing the right rule for each scenario and computing correctly, with partial credit for clear work. Interpretation earns points when each answer is translated into what it means for a decision, such as whether a review is warranted. Stating assumptions like independence, and when they might fail, adds credit. Consistent layout and labeled answers help the grader. A closing paragraph that links the problems to the unit's central idea, judging alarms against chance, usually lifts a solid set to an excellent one. In sections that allow software, a line naming the function and its inputs keeps the work checkable.
HS345 Unit 4 help from the desk
Students often multiply probabilities for events that are not independent, or add probabilities for events that can occur together. Another frequent error is reading a conditional probability backward, confusing the chance of a positive test given disease with the chance of disease given a positive test. Some sets give correct numbers with no interpretation at all. Others treat a small probability as proof that something went wrong. Rounding binomial terms too early can shift the final answer. If your set uses other scenarios, perhaps medication errors or screening programs, share the problems and the rules can be matched and interpreted one at a time. Leaving a probability as a bare decimal, without saying what it means for the infection team or the dashboard, forfeits easy interpretation points.
Get an HS345 Unit 4 example written to your instructions
Every HS345 Unit 4 set uses its own scenarios, and the custom version solves those in your prompt, not these five. Along with the problems, include the rubric and any table or data the set supplies. The first sample is free and returns within 24-48 hours, with each rule named, each complement shown and every answer read back in plain words. The paper above is an original model document written by our desk, not a submitted student paper and not an official Purdue University Global document.
More HS345 papers and BS in Health Science samples
- HS345 Unit 1: Average Versus Distribution Post
- HS345 Unit 2: Descriptive Statistics Exercise
- HS345 Unit 3: Data Display Critique
- HS345 Unit 5: Sampling Distribution Exercise
- HS345 Unit 6: Confidence Interval Problem
- HS345 Unit 7: Seminar Reflection
- HS345 Unit 8: Hypothesis Test Writeup
- HS345 Unit 9: Regression Exercise
- HS345 Unit 10: Statistical Analysis Report
- HS340 Unit 4: Two by Two Table
- HS315 Unit 4: Prevention Level Comparison
- HS450 Unit 4: Mission and Vision Critique
- HS305 Unit 4: Research Question Draft
HS345 Unit 4 questions, answered
Why does the readmission problem avoid saying skilled nursing causes readmissions?
Because patients are not assigned to destinations at random. People discharged to skilled nursing are usually older and sicker, and that alone would raise their readmission probability. The table shows the two variables are not independent, which is a statement about association. Explaining the gap would require data on how ill each group was at discharge.
Where can I find a free HS345 Unit 4 sample paper?
Read the complete Unit 4 problem set here, five applied probability problems from readmissions to a quality dashboard.
Why do dashboards with many indicators show false alarms so often?
Each indicator has a small chance of crossing its limit by chance, and those chances add up across many indicators, so at least one red flag becomes likely even when every process is stable.
What does the complement rule do?
It finds the probability that something happens at least once by subtracting the probability that it never happens from one.
Does a low probability prove a cluster is real?
No. It shows the result would be unusual if nothing had changed, which justifies a review, but chance and other explanations still have to be ruled out.