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In a survey, 70% of people like tea and 30% like coffee. If a person is chosen a

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Question: In a survey, 70% of people like tea and 30% like coffee. If a person is chosen at random, what is the probability that they like tea given that they do not like coffee?

Options:

  1. 1/3
  2. 2/3
  3. 1/2
  4. 1

Correct Answer: 1

Solution: 

If a person does not like coffee, they must like tea. Therefore, P(Tea | Not Coffee) = 1.

In a survey, 70% of people like tea and 30% like coffee. If a person is chosen a

Practice Questions

Q1
In a survey, 70% of people like tea and 30% like coffee. If a person is chosen at random, what is the probability that they like tea given that they do not like coffee?
  1. 1/3
  2. 2/3
  3. 1/2
  4. 1

Questions & Step-by-Step Solutions

In a survey, 70% of people like tea and 30% like coffee. If a person is chosen at random, what is the probability that they like tea given that they do not like coffee?
Correct Answer: 1
  • Step 1: Understand the survey results. 70% of people like tea and 30% like coffee.
  • Step 2: Recognize that if a person does not like coffee, they must like tea because those are the only two options given.
  • Step 3: Since all people who do not like coffee must like tea, the probability that a person likes tea given that they do not like coffee is 1.
  • Conditional Probability – The probability of an event occurring given that another event has already occurred.
  • Complementary Events – Understanding that if one event occurs, the other cannot, especially in mutually exclusive scenarios.
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