# A beverage plant has three lines (line A, line B and line C) for bottling the beverages. Line A bottles at a rate of 800 per hour, of which 5 percent have short fill; Line B bottles at a rate of 700 per hour, of which 3 percent have short fill; Line C bottles at a rate of 500 per hour, of which 2 percent have short fill. The lines operate for the same number of hours per day. A bottle selected at random from the production is found to have short fill. What are the probabilities that this bottle comes from line A, line B, or line C?

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A beverage plant has three lines (line A, line B and line C) for bottling the beverages. Line A bottles at a rate of 800 per hour, of which 5 percent have short fill; Line B bottles at a rate of 700 per hour, of which 3 percent have short fill; Line C bottles at a rate of 500 per hour, of which 2 percent have short fill. The lines operate for the same number of hours per day. A bottle selected at random from the production is found to have short fill. What are the probabilities that this bottle comes from line A, line B, or line C?

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Step 1

Let A be the event of selecting line A, B be the event of sleeting line B and C be the event of selecting line C.

Since there are three lines in a beverage plant, hence the probability of selecting any line is equally likely and mutually exclusive.

Step 2

It is given that the line A has 5 percent short fill bottles, line B has 3 percent short fill bottles and Line C has 2 percent short fill bottles.

Let S be the event that the selected bottle is short fill, then the priory probability are,

Step 3

The probability that the short fill bo...

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