Question

The probability of a successful optical alignment in an assembly of an optical data storage product is 0.83. What is the probability that the first successful alignment requires at most four trials

Answer 1

The probability that the first successful alignment requires at most four trials is 0.0064 and can be obtained using geometric probability.

Given:

p=0.8

Using the formula of geometric probability:

$P(X=k)=q^{k-1}p=(1-p)^{k-1}p$

a. Evaluate the definition at k=4:

$P(X=4) = (1-0.8)^{4-1} \times 0.8\\ P(X=4) = 0.2^3 \times 0.8\\ P(X=4) =0.0064$

What is geometric probability?

• The idea that probability models that are invariant under particular transformation groups are those that are mathematically natural arises from geometric probability.
• A sophisticated subset of multivariate calculus, this topic emphasizes the methodical construction of formulas for computing anticipated values associated with geometric objects produced from random points. The random geometrical objects themselves are highlighted in geometric probability.
• For instance, many models for randomly generated lines or plane tessellations; random sets produced by making the points of a spatial Poisson process, for example, the centers of discs.

To learn more about geometric probability with the given link

brainly.com/question/17514579

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