In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is

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Question: 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?

Options:

Correct Answer: 4/5

Solution:

Using the principle of inclusion-exclusion, P(Tea or Coffee) = P(Tea) + P(Coffee) - P(Both) = (30/50) + (20/50) - (10/50) = 40/50 = 4/5.

In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is

Practice Questions

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?

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).
Step 10: Simplify the expression: (30 + 20 - 10) / 50 = 40/50.
Step 11: Reduce the fraction: 40/50 = 4/5.

Inclusion-Exclusion Principle – A method used to calculate the probability of the union of two events by accounting for their overlap.
Probability Calculation – Understanding how to express the number of favorable outcomes over the total number of outcomes.
Set Theory – Basic concepts of sets, including intersections and unions, relevant for solving problems involving groups.

In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is

What’s inside this PDF?

In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is

Practice Questions

Questions & Step-by-Step Solutions

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