Question

rashaad owns a small business selling used books. he knows that in the last week 13 customers paid cash, 50 customers used a debit card, and 53 customers used a credit card. based on these results, express the probability that the next customer will pay with a debit card as a fraction in simplest form.

Explanation:

Step1: Calculate total number of customers

To find the total number of customers, we add the number of customers who paid cash, used a debit card, and used a credit card. So, \(13 + 50 + 53\).
\(13+50 = 63\), then \(63 + 53 = 116\). So the total number of customers is \(116\).

Step2: Calculate probability of debit card payment

The probability of an event is the number of favorable outcomes (customers who used debit card) divided by the total number of outcomes (total customers). The number of customers who used debit card is \(50\), and total customers is \(116\). So the probability is \(\frac{50}{116}\).

Step3: Simplify the fraction

To simplify \(\frac{50}{116}\), we find the greatest common divisor (GCD) of \(50\) and \(116\). The factors of \(50\) are \(1, 2, 5, 10, 25, 50\) and factors of \(116\) are \(1, 2, 4, 29, 58, 116\). The GCD is \(2\). Divide both numerator and denominator by \(2\): \(\frac{50\div2}{116\div2}=\frac{25}{58}\).

Answer:

\(\frac{25}{58}\)