To solve the problem of finding the probability that a customer ordered a large drink given that they ordered a hot drink, we need to use the concept of conditional probability.
Conditional probability is given by the formula:
[tex]\[
P(A \mid B) = \frac{P(A \cap B)}{P(B)}
\][/tex]
where:
- \(P(A \mid B)\) is the probability of event \(A\) occurring given that \(B\) has occurred.
- \(P(A \cap B)\) is the probability of both events \(A\) and \(B\) occurring.
- \(P(B)\) is the probability of event \(B\) occurring.
In this particular problem:
- Event \(A\) is the event that a customer orders a large drink.
- Event \(B\) is the event that a customer orders a hot drink.
From the given data:
- The number of customers who ordered large hot drinks (\(A \cap B\)) is 22.
- The total number of customers who ordered hot drinks (\(B\)) is 75.
Thus, the conditional probability \(P(\text{Large} \mid \text{Hot})\) can be calculated as follows:
[tex]\[
P(\text{Large} \mid \text{Hot}) = \frac{22}{75}
\][/tex]
To find this probability, divide 22 by 75:
[tex]\[
\frac{22}{75} \approx 0.29333333333333333
\][/tex]
We are asked to round this probability to the nearest hundredth. Therefore, 0.29333333333333333 rounded to the nearest hundredth is 0.29.
Thus, the probability that a customer ordered a large drink given that they ordered a hot drink, rounded to the nearest hundredth, is:
[tex]\[
\boxed{0.29}
\][/tex]
