A wilderness retail store asked a consulting company to do an analysis of their hiking shoe customers. The consulting company gathered data from each customer who purchased hiking shoes and recorded the shoe brand and the customer's level of happiness.The probability that a customer purchased a Toe-tastic shoe is 0.64, the probability that a customer is very pleased is 0.36, and the probability that a customer purchased a Toe-tastic shoe or is very pleased is 0.69.What is the probability that a randomly chosen customer purchased a Toe-tastic shoe and is very pleased?Write your answer as a whole number, decimal, or simplified fraction.
Question
A wilderness retail store asked a consulting company to do an analysis of their hiking shoe customers. The consulting company gathered data from each customer who purchased hiking shoes and recorded the shoe brand and the customer's level of happiness.The probability that a customer purchased a Toe-tastic shoe is 0.64, the probability that a customer is very pleased is 0.36, and the probability that a customer purchased a Toe-tastic shoe or is very pleased is 0.69.What is the probability that a randomly chosen customer purchased a Toe-tastic shoe and is very pleased?Write your answer as a whole number, decimal, or simplified fraction.
Solution
To find the probability that a randomly chosen customer purchased a Toe-tastic shoe and is very pleased, we can use the formula for the probability of the union of two events:
P(A or B) = P(A) + P(B) - P(A and B)
We know the probability of each event individually (P(A) = 0.64, P(B) = 0.36), and we know the probability of either event occurring (P(A or B) = 0.69). We can plug these values into the formula and solve for P(A and B), the probability of both events occurring:
0.69 = 0.64 + 0.36 - P(A and B)
Solving for P(A and B) gives:
P(A and B) = 0.64 + 0.36 - 0.69 = 0.31
So, the probability that a randomly chosen customer purchased a Toe-tastic shoe and is very pleased is 0.31.
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