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In a certain city, the probability of a person being a smoker is 0.3. If two peo

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Question: In a certain city, the probability of a person being a smoker is 0.3. If two people are selected at random, what is the probability that both are smokers?

Options:

  1. 0.09
  2. 0.21
  3. 0.3
  4. 0.6

Correct Answer: 0.09

Solution: 

The probability that both are smokers is 0.3 * 0.3 = 0.09.

In a certain city, the probability of a person being a smoker is 0.3. If two peo

Practice Questions

Q1
In a certain city, the probability of a person being a smoker is 0.3. If two people are selected at random, what is the probability that both are smokers?
  1. 0.09
  2. 0.21
  3. 0.3
  4. 0.6

Questions & Step-by-Step Solutions

In a certain city, the probability of a person being a smoker is 0.3. If two people are selected at random, what is the probability that both are smokers?
  • Step 1: Understand that the probability of a person being a smoker is 0.3.
  • Step 2: When selecting two people, we want to find the probability that both are smokers.
  • Step 3: Since the selection of each person is independent, we can multiply the probabilities.
  • Step 4: Calculate the probability for the first person being a smoker, which is 0.3.
  • Step 5: Calculate the probability for the second person being a smoker, which is also 0.3.
  • Step 6: Multiply the two probabilities together: 0.3 * 0.3.
  • Step 7: The result of the multiplication is 0.09, which is the probability that both selected people are smokers.
  • Independent Events – The question tests the understanding of independent events in probability, where the outcome of one event does not affect the outcome of another.
  • Multiplication Rule – It assesses the application of the multiplication rule for independent probabilities, which states that the probability of both events occurring is the product of their individual probabilities.
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