you have torn a tendon and are facing surgery to repair it. the surgeon explains the risk to you: infection occurs 3% of such operations, the repair fails in 14%, and both infection and failure occur together in 1%. what percent of these operations succeed and are free from infection?
To determine the percentage of operations that succeed and are free from infection, we need to subtract the percentages of infections and failures from 100%.
Let's break down the given information:
- Infection occurs in 3% of the operations.
- Repair failure happens in 14% of the operations.
- Both infection and failure occur together in 1% of the operations.
First, let's calculate the percentage of operations that experience either infection or failure. We can add the percentages of infection and failure and subtract the combined occurrences.
Infection or failure = Infection + Failure - (Infection and Failure)
Infection or failure = 3% + 14% - 1%
Infection or failure = 16% - 1%
Infection or failure = 15%
Now, we can find the percentage of operations that succeed and are free from infection:
Success and free from infection = 100% - (Infection or failure)
Success and free from infection = 100% - 15%
Success and free from infection = 85%
Therefore, approximately 85% of these operations succeed and are free from infection.
If portions of the 3% and 14% are not included in the 1%, then:
100% - 3% - 14% -1% = ?