Question

question: jacob owns a small business selling bagels. he knows that in the last week 108 customers paid cash, 24 customers used a debit card, and 18 customers used a credit card. based on these results, express the probability that the next customer will pay with a debit card or a credit card as a decimal to the nearest hundredth.

Explanation:

Step1: Calculate total number of customers

The total number of customers is the sum of those who paid with cash, debit - card, and credit - card. So, \(108\) (total customers), \(24\) used debit card, \(18\) used credit card, and the number of customers who paid with cash is not relevant for this probability calculation. The total number of customers who used a card (debit or credit) is \(24 + 18=42\).

Step2: Calculate probability of using a debit card

The probability \(P\) that a customer uses a debit card is the number of customers who used a debit card divided by the total number of customers. The formula for probability is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (using a debit card) is \(24\), and the total number of outcomes (total customers) is \(108\). So, \(P=\frac{24}{108}\).

Step3: Simplify the fraction and convert to decimal

\(\frac{24}{108}=\frac{2}{9}\approx0.22\) (rounded to the nearest hundredth).

Answer:

\(0.22\)