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Suppose John has a torn tendon and is facing surgery to repair it. The surgeon explains the risks to John: infection occurs in 2% of operations, the repair fails in 12% of operations, and both infection and failure occur together in 1.12% of operations. What percentage, P, of these operations succeed and are free from infection? Please round your answer to the nearest two decimal places.

Respuesta :

Answer: Our required probability is 87.12%.

Step-by-step explanation:

Since we have given that

P(infection occurs in operations ) = 2%

P(repair fails in operations ) = 12%

P(both infection and failure occur together) = 1.12%

We will first find P( infection or failure ) is given by

[tex]0.02+0.12-0.0112\\\\=0.1288\\\\=12.88\%[/tex]

So, Probability of these operations succeed and are free from infections is given by

[tex]100-12.88\\\\=87.12\%[/tex]

Hence, our required probability is 87.12%.

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