An appliance manufacturer has three factories (A, B, and C) where they produce b

Question

An appliance manufacturer has three factories (A, B, and C) where they produce both Customized and Non-Customized appliances. The weekly production totals are presented below:

If one manufactured appliance is chosen at random, find the probability that the appliance was manufactured at Factory 'A' given that it is a customized applicance.
Answer =  (Round your answer to 3 decimal places.)

Hint: Notice that the total columns are not present, so you'll want to do that first.

____________________________________________________________

Recall the delivery services example:

It is vital that a certain document reach its destination within one day. To maximize the chances of on-time delivery, two copies of the document are sent using two services, service A and service B, and the following probability table summarizes the chances of on-time delivery:

What is the probability that it was delivered on time using service B if we know service A delivered the document on time? [Table]

0.833

0.75

0.9375

0.8

0.9

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If service A has failed to deliver the document on time, what is the probability that it has arrived on time using service B?

0.5

0.05

0.15

0.0625

Explanation / Answer

1) total = 3 + 6 + 5 + 16 + 15 + 9 = 54

P(factory A | customized) = P(factory A and customized) / P(customized)

= (3/54)/((3+6+5)/54)

= 3 / 14

= 0.214

2) P(service B | service A) = P(service B and service A) / P(service A)

= 0.75/0.9

= 0.833

Option-A) 0.833

3) P(service B | service not A) = P(service B and not A) / P(service not A)

= 0.05/0.1

= 0.5

Option-A) 0.5

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