If a vaccine reduces the risk of infection by 75%, what is the probability of infection after vaccination if the initial probability of infection is 0.2? (2020)
Practice Questions
1 question
Q1
If a vaccine reduces the risk of infection by 75%, what is the probability of infection after vaccination if the initial probability of infection is 0.2? (2020)
0.05
0.1
0.15
0.2
The probability of infection after vaccination = Initial probability × (1 - reduction) = 0.2 × (1 - 0.75) = 0.2 × 0.25 = 0.05.
Questions & Step-by-step Solutions
1 item
Q
Q: If a vaccine reduces the risk of infection by 75%, what is the probability of infection after vaccination if the initial probability of infection is 0.2? (2020)
Solution: The probability of infection after vaccination = Initial probability × (1 - reduction) = 0.2 × (1 - 0.75) = 0.2 × 0.25 = 0.05.
Steps: 7
Step 1: Identify the initial probability of infection, which is given as 0.2.
Step 2: Identify the reduction in risk due to the vaccine, which is 75%.
Step 3: Convert the percentage reduction into a decimal by dividing by 100. So, 75% becomes 0.75.
Step 4: Calculate the remaining risk after vaccination by subtracting the reduction from 1. This is 1 - 0.75 = 0.25.
Step 5: Multiply the initial probability of infection (0.2) by the remaining risk (0.25). This is 0.2 × 0.25.
Step 6: Perform the multiplication: 0.2 × 0.25 = 0.05.
Step 7: The result, 0.05, is the probability of infection after vaccination.
