A company produces IC (integrated-circuit) chips. (a) The produced chips are tested one at a time until a good chip is found. If the probability that at least three tests are needed equals 0.0225. Find the defective rate (percentage of defective items) for the factory.
and solution is given as : Let the probability of finding a defective chip be p.
therefore, probability of finding a non defective chip is 1-p.
Let X be a random variable such that:
X: No of tests until a good chip is found.
or, 1-P(X<3) = 0.0225
or, (1-p) + p(1-p) =0.9775
ı did not understand part of p(x=1)=(1-p). ı think this must be just p because of geometric formulation. which one is true ? ı hope you can help me.