The marketing director of a department store interviewed 50 customers who had bought appliances the previous week. They found that 20% of the customers bought a washing machine and 40% bought a dishwasher. Also 48% of the customers bought an appliance other than a washing machine or dishwasher.
What is the probability that a surveyed customer selected at random bought both a washing machine and a dishwasher?
b. Of the 50 customers surveyed, how many were likely to have bought both a a washing machine and a dishwasher?
The question is confusing. If 20% bought washing machines and 40% bought dishwashers does it mean 40% bought both? How does 48% of the customer who bought neither washing machine nor dishwasher play a role in the problem?
boo boo
Based on the information given, we can calculate the probability of a surveyed customer selecting at random who bought both a washing machine and a dishwasher.
To find this probability, we need to determine the intersection of the events "bought a washing machine" and "bought a dishwasher". In other words, we want to find the probability of customers who bought both appliances.
Since the question does not provide information about the specific customers who bought both appliances, we can assume the events "bought a washing machine" and "bought a dishwasher" are independent.
The probability of selecting a customer who bought a washing machine is 20% or 0.2, and the probability of selecting a customer who bought a dishwasher is 40% or 0.4.
If we assume independence, we can multiply these probabilities to find the probability of a customer buying both appliances:
Probability of buying both appliances = Probability of buying a washing machine * Probability of buying a dishwasher
= 0.2 * 0.4
= 0.08 or 8%
Therefore, the probability that a surveyed customer selected at random bought both a washing machine and a dishwasher is 8%.
Regarding the second part of the question, we cannot determine the exact number of customers who bought both appliances without knowing the total number of customers surveyed.
The question is indeed a bit confusing, but we can still work through it to find the answers.
Let's break down the information given:
1. 20% of the customers bought a washing machine.
2. 40% of the customers bought a dishwasher.
3. 48% of the customers bought an appliance other than a washing machine or dishwasher.
The key information we need to find the probability of a customer buying both a washing machine and a dishwasher is missing, but we can make an assumption to solve the problem.
Assumption: Customers who bought both a washing machine and a dishwasher are included in the 20% who bought a washing machine AND in the 40% who bought a dishwasher. In other words, the percentages are not mutually exclusive.
Now, let's find the answers to the given questions:
a. Probability that a surveyed customer selected at random bought both a washing machine and a dishwasher:
Since we assumed that the percentages are not mutually exclusive, we can add the probabilities together:
P(both) = P(washing machine) + P(dishwasher) - P(neither)
P(both) = 20% + 40% - 48%
P(both) = 12%
So, the probability that a surveyed customer selected at random bought both a washing machine and a dishwasher is 12%.
b. Number of customers likely to have bought both a washing machine and a dishwasher:
To find the number of customers, we need to multiply the probability by the total number of customers surveyed:
Number of customers = P(both) * Total customers surveyed
Number of customers = 12% * 50
Number of customers = 6
Therefore, it is likely that 6 out of the 50 customers surveyed bought both a washing machine and a dishwasher.