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$Scarlett owns a small business selling ice-cream. She knows that in the last week 49 customers paid cash, 2 customers used a debit card, and 4 customers used a credit card. Based on these results, express the probability that the next customer will pay with cash as a fraction in simplest form. Answer:$

Scarlett owns a small business selling ice-cream. She knows that in the last week $49$ customers paid cash, $2$ customers used a debit card, and $4$ customers used a credit card. $\newline$ Based on these results, express the probability that the next customer will pay with cash as a fraction in simplest form. $\newline$ Answer:

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Experimental probability

Full solution

Q. Scarlett owns a small business selling ice-cream. She knows that in the last week

49

customers paid cash,

2

customers used a debit card, and

4

customers used a credit card.

\newline

Based on these results, express the probability that the next customer will pay with cash as a fraction in simplest form.

\newline

Answer:

Find Probability: To find the probability that the next customer will pay with cash, we need to determine the total number of customers and the number of customers who paid with cash.
Calculate Total Customers: The total number of customers is the sum of customers who paid with cash, debit card, and credit card. $\newline$ Total customers $= \text{Customers who paid cash} + \text{Customers who used debit card} + \text{Customers who used credit card}$ $\newline$ Total customers $= 49 \text{ (cash)} + 2 \text{ (debit card)} + 4 \text{ (credit card)}$ $\newline$ Total customers $= 55$
Calculate Probability: The probability of an event is given by the number of favorable outcomes divided by the total number of possible outcomes. In this case, the favorable outcomes are the number of customers who paid with cash. $\newline$ Probability (Paying with cash) = $\frac{\text{Number of customers who paid with cash}}{\text{Total number of customers}}$ $\newline$ Probability (Paying with cash) = $\frac{49}{55}$
Simplify Fraction: We need to simplify the fraction $\frac{49}{55}$ to its simplest form. Both $49$ and $55$ have a common factor of $1$ , and there are no other common factors since $55$ is not a multiple of $7$ . $\newline$ Therefore, the fraction is already in its simplest form.

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