Question

suppose John has a torn tendon and is facing surgery to repair it. The surgeon explains the risks to John: infection occurs in 4% of operations, the repair fails in 12% of operations, and both infection and failure occur together in 0.78% of operations. What percentage, P, of these operations succeed and are free from infection? Please round your answer to the nearest two decimal places.

Answer 1

Answer:

84.78%

Step-by-step explanation:

Data provided in the question:

P( Infection occurred ) = 4% = 0.04

P( Repair fails ) = 12% = 0.12

P( Both infection and failure occur ) = 0.78% = 0.0078

Now,

P( operations succeed and are free from infection )

= 1 - P( Failure ∪ Infection )

also,

P( Failure ∪ Infection )

= P( Infection occurred ) + P( Repair fails ) - P( Both infection and failure occur )

or

P( Failure ∪ Infection ) = 0.04 + 0.12 - 0.0078 = 0.1522

Therefore,

P( operations succeed and are free from infection )

= 1 - P( Failure ∪ Infection )

or

= 1 - 0.1522

= 0.8478

or

⇒ 0.8478 × 100% = 84.78%