How to Solve Discrete Random Variables — Univariate RV — geometric distribution Questions on Exam P
Sample Practice Problem
ID: #98OXY
Let \(N\) be the number of independent screening tests performed. Tests continue through the first positive. The expected number of tests is 8. Calculate the probability the first positive occurs on test 6.
📖 Worked Solution & Strategy
A geometric count on \(1,2,\ldots\) has mean \(1/p=8\), so test positivity probability is \(p=1/8\) and failure probability is \(q=1-p=\frac{7}{8}\). Independence makes successive failure probabilities multiply. First positive on test \(6\) requires five failures then success: \(q^5p=(\frac{7}{8})^5(1/8)=0.0641\).