can you look this problem and solution?

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.

Given that,

P(X>=3)=0.0225

or, 1-P(X<3) = 0.0225

or, P(X=1)+P(X=2)=1-0.0225=0.9775

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.

$$p(x=1)=1-p$$ is correct. If you like, you may express it as $$p(x=1)=p^0(1-p)^1=1-p$$.
• You already said "Let the probability of finding a defective chip be p", and "probability of finding a non defective chip is 1-p". Thus, $p(x=1) = p^{x-1}(1-p)^x$. – user295357 Nov 18 '20 at 14:33