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Deion owns a small business selling clothing. He knows that in the last week 45 customers paid cash, 6 customers used a debit card, and 37 customers used a credit card.
Based on these results, express the probability that the next customer will pay with cash as a decimal to the nearest hundredth.

Deion owns a small business selling clothing. He knows that in the last week $45$ customers paid cash, $6$ customers used a debit card, and $37$ customers used a credit card. $\newline$ Based on these results, express the probability that the next customer will pay with cash as a decimal to the nearest hundredth.

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Full solution

Q. Deion owns a small business selling clothing. He knows that in the last week

45

customers paid cash,

6

customers used a debit card, and

37

customers used a credit card.

\newline

Based on these results, express the probability that the next customer will pay with cash as a decimal to the nearest hundredth.

Total Number of Customers: Determine the total number of customers from last week. $\newline$ We have: $\newline$ Customers who paid cash: $45$ $\newline$ Customers who used a debit card: $6$ $\newline$ Customers who used a credit card: $37$ $\newline$ What is the total number of customers from last week? $\newline$ $45$ (cash) + $6$ (debit) + $37$ (credit) = $88$ $\newline$ Total number of customers: $88$
Probability of Cash Payment: Calculate the probability that the next customer will pay with cash. $\newline$ We have: $\newline$ Customers who paid cash: $45$ $\newline$ Total number of customers: $88$ $\newline$ What is the probability of a customer paying with cash? $\newline$ $P(\text{cash}) = \frac{\text{Number of cash customers}}{\text{Total number of customers}}$ $\newline$ $P(\text{cash}) = \frac{45}{88}$ $\newline$ Now, we need to convert this fraction to a decimal.
Convert Fraction to Decimal: Convert the fraction to a decimal and round to the nearest hundredth. $\newline$ $P(\text{cash}) = \frac{45}{88} \approx 0.51136$ $\newline$ Rounded to the nearest hundredth, this is approximately $0.51$ .

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