126 people are asked about their usual breakfast, 62 people have tea, 51 people have toast and 28 people have neither work out the probability a person chosen at random have both tea and toast

To find the probability that a person chosen at random has both tea and toast, we can use the principle of inclusion-exclusion. 1. Total number of people surveyed: 126 2. People who have tea: 62 3. People who have toast: 51 4. People who have neither: 28 First, we find the number of people who have either tea or toast or both: \[ People who have either tea or toast = Total - Neither = 126 - 28 = 98 \] Using the inclusion-exclusion principle: \[ People who have tea or toast = People with tea + People with toast - People with both \] Let \( x \) be the number of people who have both tea and toast: \[ 98 = 62 + 51 - x \] Solving for \( x \): \[ 98 = 113 - x \\ x = 113 - 98 \\ x = 15 \] Now, the probability that a person chosen at random has both tea and toast is: \[ Probability = Number of people with bothTotal number of people = (15)/(126) = (5)/(42) \] Thus, the probability is \( (5)/(42) \).