Advanced Mathematics

10. (15 points total)Small hard particles are found in the molten glass from which glass bottles are made. On average 20 particles are found in 100 kg of molten glass. The distribution of these particle sis Poisson. If a bottle made of this glass contains one or more such particles it has to be discarded. Bottles of mass 1 kg are made using this glass.

What is the probability that a randomly chosen bottle needs to be discarded?

(b) (5 points) Using the expression above for the probability that a randomly chosen bottle is defective, determine the probability that in a randomly chosen batch of 10 bottles, 4out of the 10 are defective?

(c) (5 points) Suppose you randomly sample the bottles one by one, what is the probability that the first defective bottle found is the 5th sample?



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