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If a disease has a 10% chance of transmission per contact, what is the probabili

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Question: If a disease has a 10% chance of transmission per contact, what is the probability of not transmitting the disease after 3 contacts? (2022)

Options:

  1. 0.729
  2. 0.8
  3. 0.9
  4. 0.1

Correct Answer: 0.729

Exam Year: 2022

Solution: 

Probability of not transmitting in one contact = 1 - 0.1 = 0.9. For 3 contacts, it is 0.9^3 = 0.729.

If a disease has a 10% chance of transmission per contact, what is the probabili

Practice Questions

Q1
If a disease has a 10% chance of transmission per contact, what is the probability of not transmitting the disease after 3 contacts? (2022)
  1. 0.729
  2. 0.8
  3. 0.9
  4. 0.1

Questions & Step-by-Step Solutions

If a disease has a 10% chance of transmission per contact, what is the probability of not transmitting the disease after 3 contacts? (2022)
  • Step 1: Understand that the disease has a 10% chance of being transmitted per contact.
  • Step 2: Calculate the probability of not transmitting the disease in one contact. This is done by subtracting the transmission chance from 1: 1 - 0.1 = 0.9.
  • Step 3: Since we want to find the probability of not transmitting the disease after 3 contacts, we need to multiply the probability of not transmitting in one contact by itself three times: 0.9 * 0.9 * 0.9.
  • Step 4: This can be simplified using exponents: 0.9^3.
  • Step 5: Calculate 0.9^3, which equals 0.729.
  • Probability of Independent Events – The question tests the understanding of calculating the probability of independent events occurring multiple times, specifically using the complement rule.
  • Complement Rule – It assesses the ability to apply the complement rule, where the probability of an event not occurring is calculated as 1 minus the probability of the event occurring.
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