Score: \( 0 / 100 \) Answered: \( 0 / 20 \) Question 1 A survey asks 136 people "What beverage do you drink in the morning?", and offers choices: - Coffee only - Both tea and coffee - Neither tea nor coffee Suppose 44 report tea only, 24 report coffee only, and 28 report both. How many people drink tea in the morning? How many people drink coffee in the morning? Hany people drink neither tea nor coffee? Hots

To solve this problem, we can use the principle of inclusion-exclusion. Let's denote the following: - \( T \) as the number of people who drink tea only - \( C \) as the number of people who drink coffee only - \( B \) as the number of people who drink both tea and coffee - \( N \) as the number of people who drink neither tea nor coffee We are given the following information: - \( T = 44 \) - \( C = 24 \) - \( B = 28 \) - Total number of people surveyed = 136 We can use the principle of inclusion-exclusion to find the number of people who drink tea, coffee, and neither: - Number of people who drink tea = \( T + B \) - Number of people who drink coffee = \( C + B \) - Number of people who drink neither = Total number of people - (Number of people who drink tea + Number of people who drink coffee) Let's calculate these values. Calculate the value by following steps: - step0: Calculate: \(44+28\) - step1: Add the numbers: \(72\) The number of people who drink tea in the morning is 72. Now, let's calculate the number of people who drink coffee in the morning. Calculate the value by following steps: - step0: Calculate: \(24+28\) - step1: Add the numbers: \(52\) The number of people who drink coffee in the morning is 52. Finally, let's calculate the number of people who drink neither tea nor coffee. Calculate the value by following steps: - step0: Calculate: \(136-\left(72+52\right)\) - step1: Add the numbers: \(136-124\) - step2: Subtract the numbers: \(12\) The number of people who drink neither tea nor coffee is 12. Therefore, the answers to the questions are: - Number of people who drink tea in the morning: 72 - Number of people who drink coffee in the morning: 52 - Number of people who drink neither tea nor coffee: 12