Question 2 A survey asked 248 people what alternative transportation modes they use. The results are below. 167 walk 139 use the bus 108 ride a bicycle 93 walk and use the bus 75 walk and ride a bicycle 64 ride the bus and ride a bicycle 45 said they use all three modes of transportation How many people only ride the bus? How many people don't use any alternate transportation?

To solve this problem, we can use the principle of inclusion-exclusion. Let's denote the following: - \( W \) = number of people who walk - \( B \) = number of people who use the bus - \( C \) = number of people who ride a bicycle - \( W \cap B \) = number of people who walk and use the bus - \( W \cap C \) = number of people who walk and ride a bicycle - \( B \cap C \) = number of people who ride the bus and ride a bicycle - \( W \cap B \cap C \) = number of people who use all three modes of transportation We are given the following information: - \( W = 167 \) - \( B = 139 \) - \( C = 108 \) - \( W \cap B = 93 \) - \( W \cap C = 75 \) - \( B \cap C = 64 \) - \( W \cap B \cap C = 45 \) We need to find: 1. Number of people who only ride the bus 2. Number of people who don't use any alternate transportation Let's calculate these values step by step: 1. Number of people who only ride the bus: - Number of people who only ride the bus = \( B - (W \cap B) - (B \cap C) + (W \cap B \cap C) \) 2. Number of people who don't use any alternate transportation: - Number of people who don't use any alternate transportation = Total number of people - (Number of people who walk + Number of people who use the bus + Number of people who ride a bicycle - (Number of people who walk and use the bus + Number of people who walk and ride a bicycle + Number of people who ride the bus and ride a bicycle) + Number of people who use all three modes of transportation) Let's calculate these values. Calculate the value by following steps: - step0: Calculate: \(139-93-64+45\) - step1: Calculate: \(27\) 1. Number of people who only ride the bus = 27 Now, let's calculate the number of people who don't use any alternate transportation. Calculate the value by following steps: - step0: Calculate: \(248-\left(167+139+108-\left(93+75+64\right)+45\right)\) - step1: Add the numbers: \(248-\left(167+139+108-232+45\right)\) - step2: Calculate: \(248-227\) - step3: Subtract the numbers: \(21\) 2. Number of people who don't use any alternate transportation = 21 Therefore, the number of people who only ride the bus is 27, and the number of people who don't use any alternate transportation is 21.