Question

At a local coffee shop, 10% of customers order decaf coffee and 30% are students. Given that 5% of students order decaf coffee, what is the probability that a randomly selected customer is a student AND orders decaf coffee? Round to 3 decimal places.

Answer 1

The probability that a randomly selected customer is both a student and orders decaf coffee is calculated by multiplying the probability of a customer being a student by the probability that a student orders decaf. The result is 1.5%.

Step-by-step explanation:

We're given that 10% of customers order decaf coffee, 30% are students, and among the students, 5% order decaf coffee. To find the probability that a randomly selected customer is both a student and orders decaf, we need to use the concept of joint probability. Joint probability is found by multiplying the probability of one event by the conditional probability of the second event, given the first event.

The probability of a randomly selected customer being a student is 0.30. The probability that a student orders decaf, given they are a student, is 0.05. We multiply these probabilities to get the joint probability:

P(Student and Decaf) = P(Student) x P(Decaf | Student) = 0.30 x 0.05 = 0.015

The probability that a randomly selected customer is a student and orders decaf coffee is therefore 0.015, or 1.5%, when rounded to three decimal places.

Answer 2

0.015

Step-by-step explanation:

We know that 30% of the customers are students, and 5% of these students order decaf coffee, so we can say that 5% of that 30% (=1.5%) is the percentage of customers that are students and order decaf coffee.

So, the probability of randomly selecting a customer that is a student and orders decaf coffee is 1.5% = 0.015

The percentage of customers that order decaf coffee (10%) is not applied in this solution, as we can have the percentage of students that order decaf coffee just using the percentage of customers that are students, and the percentage of students that order decaf coffee.