Introduction

There are two common cups of coffee and four cups of tea on the counter. Hilowle decides to drink two of them. What is the probability that both cups he drinks are coffee?

Understanding the Problem

The problem does not provide enough information to directly state the probability, as it depends on Hilowle's preferences and habits. For instance, Hilowle might prefer tea to coffee, or he may prefer to switch drinks if the first one is coffee. However, we can make a mathematical assumption to approach the problem.

Assumptions and Calculations

If we assume that Hilowle chooses each cup with equal probability from the remaining alternatives, we can proceed with this simplified model. Here’s the step-by-step calculation:

Step 1: Probability of the First Drink being Coffee

P(first drink is coffee) 2/6 1/3

Step 2: Probability of the Second Drink being Coffee Given the First Was Coffee

After drinking one cup of coffee, there are now 5 drinks left, with 1 coffee and 4 tea. P(second drink is coffee | first drink was coffee) 1/5

Step 3: Combined Probability

The total probability that Hilowle drinks two cups of coffee is the product of the probabilities from the above steps: P(two cups of coffee) (1/3) * (1/5) 1/15

Therefore, the probability that Hilowle drinks two cups of coffee is 1/15.

What is the Probability This is a Homework Problem?

The problem can be framed as a homework question, with several key hints and steps:

Hint 1: Probability of First Drink Being Coffee

Question: What is the probability that Hilowle’s first drink is a cup of coffee?

Answer: P(first drink is coffee) 2/6 1/3

Hint 2: Probability Assuming First Drink Was Coffee

Assumption: If the first drink is coffee, there are now 5 drinks left: 1 coffee and 4 tea.

Question: Assuming his first drink was coffee, what is the probability of his second drink also being coffee?

Answer: P(second drink is coffee | first drink was coffee) 1/5

Combining Probabilities

Question: How do you combine these probabilities to find the overall probability?

Answer: The overall probability is the product of the individual probabilities: P(two cups of coffee) (1/3) * (1/5) 1/15

By following these steps and combining the probabilities, you can solve the problem of determining the likelihood that Hilowle drinks two cups of coffee.