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If a person has a 20% chance of contracting a disease and a 30% chance of recove

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Question: If a person has a 20% chance of contracting a disease and a 30% chance of recovery, what is the probability that the person will contract the disease and not recover? (2022)

Options:

  1. 0.14
  2. 0.06
  3. 0.1
  4. 0.2

Correct Answer: 0.14

Exam Year: 2022

Solution: 

Probability of contracting and not recovering = Probability of contracting × (1 - Probability of recovery) = 0.20 × (1 - 0.30) = 0.20 × 0.70 = 0.14.

If a person has a 20% chance of contracting a disease and a 30% chance of recove

Practice Questions

Q1
If a person has a 20% chance of contracting a disease and a 30% chance of recovery, what is the probability that the person will contract the disease and not recover? (2022)
  1. 0.14
  2. 0.06
  3. 0.1
  4. 0.2

Questions & Step-by-Step Solutions

If a person has a 20% chance of contracting a disease and a 30% chance of recovery, what is the probability that the person will contract the disease and not recover? (2022)
  • Step 1: Identify the probability of contracting the disease, which is 20%. Convert this percentage to a decimal: 20% = 0.20.
  • Step 2: Identify the probability of recovery, which is 30%. Convert this percentage to a decimal: 30% = 0.30.
  • Step 3: Calculate the probability of not recovering. This is done by subtracting the probability of recovery from 1: 1 - 0.30 = 0.70.
  • Step 4: Now, multiply the probability of contracting the disease (0.20) by the probability of not recovering (0.70): 0.20 × 0.70.
  • Step 5: Perform the multiplication: 0.20 × 0.70 = 0.14.
  • Step 6: The final result, 0.14, represents the probability that the person will contract the disease and not recover.
  • Probability Calculation – Understanding how to calculate the probability of two dependent events occurring, specifically contracting a disease and not recovering.
  • Complementary Probability – Using the concept of complementary probability to find the chance of not recovering from the disease.
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