At a coffee shop, 55% of the customers buy a coffee drink, 30% buy food, and 25% buy both a coffee drink and food.
What is the probability that a randomly chosen customer buys either a coffee drink or food?
To find the probability that a randomly chosen customer buys either a coffee drink or food, we can add the probabilities of each event and subtract the probability of buying both.
Let's define:
A = event of buying a coffee drink
B = event of buying food
Given:
P(A) = 55%
P(B) = 30%
P(A ∩ B) = 25% (buying both a coffee drink and food)
To find P(A ∪ B) (the probability of buying either a coffee drink or food), we can use the formula:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
P(A ∪ B) = 55% + 30% - 25%
P(A ∪ B) = 85% - 25%
P(A ∪ B) = 60%
Therefore, the probability that a randomly chosen customer buys either a coffee drink or food is 60%.