Given the problem, we need to interpret what [tex]\( P(A \cup B) = 0.60 \)[/tex] means in terms of the scenario with the food truck.
Let’s break it down step by step:
1. Define the Events:
- Let event [tex]\( A \)[/tex] be the event that a customer buys a taco.
- Let event [tex]\( B \)[/tex] be the event that a customer buys a drink.
2. Probability Notation:
- [tex]\( P(A) \)[/tex] is the probability that a customer buys a taco.
- [tex]\( P(B) \)[/tex] is the probability that a customer buys a drink.
- [tex]\( P(A \cup B) \)[/tex] is the probability that a customer buys either a taco, a drink, or both.
3. Interpreting [tex]\( P(A \cup B) = 0.60 \)[/tex]:
- The union of events [tex]\( A \)[/tex] and [tex]\( B \)[/tex], denoted as [tex]\( A \cup B \)[/tex], represents the event that a customer buys either a taco, a drink, or both.
- [tex]\( P(A \cup B) = 0.60 \)[/tex] means that there's a 60% chance that a customer will purchase either a taco, a drink, or both.
Now we evaluate the given options:
- Option A: This option states that buying a taco and buying a drink are mutually exclusive events. This would mean that a customer can't buy both a taco and a drink at the same time. However, this is not related to the information given by [tex]\( P(A \cup B) \)[/tex].
- Option B: This option states that the probability that a customer buys a taco, a drink, or both is 60%. This directly matches the interpretation of [tex]\( P(A \cup B) = 0.60 \)[/tex].
- Option C: This option states that the probability that a customer buys both a taco and a drink is 60%. This would refer to [tex]\( P(A \cap B) \)[/tex], which isn't what's given in the problem.
- Option D: This option states that the probability that a customer buys neither a taco nor a drink is 60%. This would relate to [tex]\( P((A \cup B)') \)[/tex], or [tex]\( 1 - P(A \cup B) \)[/tex], which would be 0.40, not 0.60.
Therefore, the correct interpretation in this problem is:
Answer: B. The probability that a customer buys a taco, a drink, or both is 60%.
