Socceroos Ltd manufactures World Cup soccer balls in 2 models: premium and standard. An auditor engaged in a compliance audit of the firm is validating the sales account for April. She has collected 200 invoices for the month. 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,

D. Find the following probabilities that an invoice for the premium model given that it’s a retail invoice.

and record the probability in percentage

Question

Socceroos Ltd manufactures World Cup soccer balls in 2 models: premium and standard. An auditor engaged in a compliance audit of the firm is validating the sales account for April. She has collected 200 invoices for the month. 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,

D. Find the following probabilities that an invoice for the premium model given that it’s a retail invoice.

and record the probability in percentage

BlackTom AI · Accepted Answer

We start by identifying the given counts relevant to the conditional probability.
- Total invoices: 200
- Total retail invoices: 140
- Retail invoices for the standard model: 28
From these, we can deduce the number of premium model invoices within the retail category.
- Retail premium invoices = Retail total − Retail standard = 140 − 28 = 112
The probability asked is: P(Premium | Retail) = (Number of premium retail invoices) / (Total retail invoices).
- P(Premium | Retail) = 112 / 140
We simplify the fraction: 112 ÷ 140 = 0.8
Convert to percentage by multiplying by 100: 0.8 × 100 = 80%
Thus, the probability that an invoice is for the premium model given that it is a retail invoice is 80%.

BRED001 Week 3 Practice Quiz

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