Isaac, a manager at a supermarket, is inspecting cans of pasta to make sure that the cans are neither dented nor have other defects. From past experience, he knows that 1 can in every 90 is defective. What is the probability that Isaac will find his first defective can among the first 50 cans

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02-03-2020
Mathematics

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Isaac, a manager at a supermarket, is inspecting cans of pasta to make sure that the cans are neither dented nor have other defects. From past experience, he knows that 1 can in every 90 is defective. What is the probability that Isaac will find his first defective can among the first 50 cans

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ChiKesselman ChiKesselman · Answer 1 · 2020-03-03T05:13:27+01:00

Answer:

0.0064 is the probability that Isaac will find his first defective can among the first 50 cans.

Step-by-step explanation:

W are given the following in the question:

Probability of defective can =

[tex]P(A) = \dfrac{1}{90}[/tex]

We have to find the probability that Isaac will find his first defective can among the first 50 cans.

Then the number of adults follows a geometric distribution, where the probability of success on each trial is p, then the probability that the kth trial (out of k trials) is the first success is

[tex]P(X=k) = (1-p)^{k-1}p[/tex]

We have to evaluate:

[tex]P(x = 50)\\= (1-\frac{1}{90})^{50-1}(\frac{1}{90})\\= 0.0064[/tex]

0.0064 is the probability that Isaac will find his first defective can among the first 50 cans.