In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is the probability that a randomly selected person likes either tea or coffee?
Practice Questions
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Q1
In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is the probability that a randomly selected person likes either tea or coffee?
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Using the principle of inclusion-exclusion, the number of people who like either tea or coffee is 30 + 20 - 10 = 40. The probability is 40/50 = 0.8.
Questions & Step-by-step Solutions
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Q
Q: In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is the probability that a randomly selected person likes either tea or coffee?
Solution: Using the principle of inclusion-exclusion, the number of people who like either tea or coffee is 30 + 20 - 10 = 40. The probability is 40/50 = 0.8.
Steps: 7
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: Use the principle of inclusion-exclusion to find the number of people who like either tea or coffee. This is calculated as: (Number of tea lovers) + (Number of coffee lovers) - (Number of people who like both). So, 30 + 20 - 10 = 40.
Step 6: Now, to find the probability that a randomly selected person likes either tea or coffee, divide the number of people who like either by the total number of people. This is 40 divided by 50.
