At a gas station, 84% of customers buy gasoline, 9% of customers buy gasoline and a beverage, and 5% of customers buygasoline and a snack.a. What is the probability that a customer who buys gasoline also buys a beverage? Express your first answer as a simplified fraction and your percent answer rounded to the tenths place. , or about $\%$%b. What is the probability that a customer who buys gasoline also buys a snack? Express your first answer as a simplified fraction and your percent answer rounded to the tenths place. , or about $\%$
Question
At a gas station, 84% of customers buy gasoline, 9% of customers buy gasoline and a beverage, and 5% of customers buygasoline and a snack.a. What is the probability that a customer who buys gasoline also buys a beverage? Express your first answer as a simplified fraction and your percent answer rounded to the tenths place. , or about %b. What is the probability that a customer who buys gasoline also buys a snack? Express your first answer as a simplified fraction and your percent answer rounded to the tenths place. , or about
Solution
a. The probability that a customer who buys gasoline also buys a beverage is calculated by dividing the percentage of customers who buy both gasoline and a beverage by the total percentage of customers who buy gasoline.
So, the calculation would be 9% (gasoline and beverage) divided by 84% (gasoline).
9/84 = 0.1071 as a decimal.
To convert this to a fraction, we know that 0.1071 is approximately 1071/10000. However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 1071.
So, 1071/10000 = 1/9.35, which simplifies further to approximately 1/9.
Therefore, the probability that a customer who buys gasoline also buys a beverage is 1/9, or about 10.7%.
b. The probability that a customer who buys gasoline also buys a snack is calculated in a similar way.
We divide the percentage of customers who buy both gasoline and a snack by the total percentage of customers who buy gasoline.
So, the calculation would be 5% (gasoline and snack) divided by 84% (gasoline).
5/84 = 0.0595 as a decimal.
To convert this to a fraction, we know that 0.0595 is approximately 595/10000. However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 595.
So, 595/10000 = 1/16.8, which simplifies further to approximately 1/17.
Therefore, the probability that a customer who buys gasoline also buys a snack is 1/17, or about 5.9%.
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