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 statistician hired by the company to investigate the level of contamination in the stored cartridges found that 25% of the cartridges in 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 p1x2 = 1.2521.752x - 1, x = 1, 2, 3, c

a. Find p122. Interpret this result.

b. Find p142. Interpret this result.

c. Find P1x Ú 22. Interpret this result.