Find the indicated probabilities using the geometric distribution, the Poisson d

Question

Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the distribution. Then determine use the appropriate probability table or technology to find the probabilities. A glass manufacturer fields that 1 in 250 glass items produced is Find the probability that (a) the first (a) P(the first warped glass item in the 11^th item produced) = (Round to three decimal places as needed.) (b) P(the first warped glass item in the first, second, or third item produced) = (Round to three decimal places as needed.) (c) P(none of the first 10 glass items produced are defective) = (Round to three decimal places as reduced.)

Explanation / Answer

Solution:

The probability of any item being warped is 1/250, but if you want to know the probability of a particular one being warped, it's 1/[250-(n-1)]
because you're assuming you haven't hit that one warped one yet.

a) n = 11, (n - 1) = 10, so the probability is 1/(240) = 1/240

b) Solve for n = 1, 2 and 3==> 0.04,1/249,1/248

c) All of the first ten are warped, so you multiply the basic probability ten times
= (1/250)n
In this case n = 10
= (1/250)10

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