A survey was made of 100 customers in a department store. 70 of the customers indicated they visited the store because of a newspaper advertisement. The remainder had not seen the ad. A total of 40 customers made purchases; of these customers, 30 had seen the ad. What is the probability that a customer who saw the ad. made a purchase?
i have no clue how to do this
To find the probability that a customer who saw the ad made a purchase, we need to use the concept of conditional probability. Conditional probability measures the likelihood of an event occurring given that another event has already occurred.
Let's denote the following events:
A = Customer made a purchase
B = Customer saw the ad
The conditional probability we are looking for is the probability of event A (customer made a purchase) given event B (customer saw the ad), which can be written as P(A|B).
We know that 40 customers made purchases, and out of those 40, 30 had seen the ad. This means that P(A and B), the probability that a customer made a purchase and saw the ad, is 30/100 (since the survey was conducted on 100 customers).
The probability that a customer saw the ad, P(B), is given as 70/100 (since 70 out of 100 customers saw the ad).
Using these probabilities, we can apply the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
Plugging in the values:
P(A|B) = (30/100) / (70/100) = 30/70 = 3/7 ≈ 0.4286
Therefore, the probability that a customer who saw the ad made a purchase is approximately 0.4286.