In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is
Practice Questions
Q1
In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is the probability that a person chosen at random likes either tea or coffee?
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Questions & Step-by-Step Solutions
In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is the probability that a person chosen at random likes either tea or coffee?
Step 1: Identify the total number of people in the group, which is 50.
Step 2: Identify how many people like tea, which is 30.
Step 3: Identify how many people like coffee, which is 20.
Step 4: Identify how many people like both tea and coffee, which is 10.
Step 5: Calculate the probability of liking tea, which is the number of tea lovers divided by the total number of people: 30/50.
Step 6: Calculate the probability of liking coffee, which is the number of coffee lovers divided by the total number of people: 20/50.
Step 7: Calculate the probability of liking both tea and coffee, which is the number of people who like both divided by the total number of people: 10/50.
Step 8: Use the principle of inclusion-exclusion to find the probability of liking either tea or coffee: P(Tea or Coffee) = P(Tea) + P(Coffee) - P(Both).
Step 9: Substitute the probabilities into the formula: (30/50) + (20/50) - (10/50).
