Question 1184373: A & B Pty Ltd manufactures window air-conditioners in both a
deluxe model and a standard model. An auditor undertaking a
compliance audit of the firm is validating the sales account for
April. She has collected 200 invoices for the month, some of which
were sent to wholesalers and the remainder to retailers. Of the
140 retail invoices, 28 are for the standard model. Of the
wholesale invoices, 24 are for the standard model. If the auditor
selects one invoice at random, find the probability that:
a) the invoice selected is for the deluxe model .
b) the invoice selected is wholesale invoice for the deluxe model
c) the invoice selected is either a wholesale invoice or an invoice
for the standard model
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the probabilities:
First, let's organize the data into a table:
| Invoice Type | Deluxe Model | Standard Model | Total |
|---|---|---|---|
| Retail | 140 - 28 = 112 | 28 | 140 |
| Wholesale | 200 - 140 - 24 = 36 | 24 | 60 |
| Total | 112 + 36 = 148 | 28 + 24 = 52 | 200 |
**a) Probability of a Deluxe Model Invoice:**
* There are 148 deluxe model invoices out of a total of 200 invoices.
* P(Deluxe) = 148/200 = 0.74 or 74%
**b) Probability of a Wholesale Invoice for the Deluxe Model:**
* There are 36 wholesale invoices for the deluxe model.
* P(Wholesale and Deluxe) = 36/200 = 0.18 or 18%
**c) Probability of a Wholesale Invoice or a Standard Model Invoice:**
We can use the addition rule for probability:
P(Wholesale or Standard) = P(Wholesale) + P(Standard) - P(Wholesale and Standard)
* P(Wholesale) = 60/200 = 0.30
* P(Standard) = 52/200 = 0.26
* P(Wholesale and Standard) = 24/200 = 0.12
P(Wholesale or Standard) = 0.30 + 0.26 - 0.12 = 0.44 or 44%
Alternatively, we can count the number of invoices that are either wholesale or for the standard model (or both):
* Wholesale: 60
* Standard: 52
* Both: 24
So, 60 + 52 - 24 = 88 invoices are either wholesale or standard (or both).
Then P(Wholesale or Standard) = 88/200 = 0.44 or 44%
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