Chapter 4.2, Problem 4.29ACI

Contaminated gun cartridges. A weapons manufacturer uses a liquid propellant to produce gun cartridges. During the manufacturing process, the propellant can get mixed with another liquid to produce a contaminated cartridge. A University of South Florida statistician, hired by the company to investigate the level of contamination in the stored cartridges, found that 23% of the cartridges in a particular lot were contaminated. Suppose you randomly sample (without replacement) gun cartridges from this lot until you find a contaminated one. Let x be the number of cartridges sampled until a contaminated one is found. It is known that the probability distribution for x is given by the formula

     $p(x)=(.23){(.77)}^{x-1},x=1,2,3,\dots$

1. a. Find p(1). Interpret this result.
2. b. Find p(5). Interpret this result.
3. c. Find P(x ≥ 2). Interpret this result.