Question

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 1.35% 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

Explanation:

The total number of operations prepared by the surgeon is X.

The questions can be solved by set

For two sets A and B,

Where A= The surgery done with infections

B= Surgery done which failed

n(AᴜB) is the number of elements present in either of the sets A or B.

n(A∩B) is the number of elements present in both the sets A and B.

Y= number of surgery which succeed and are free from infection

n(AᴜB) = n(A) + (n(B) – n(A∩B) + Y

X= 2% of X + 12% of X -1.35% of x + Y

X=0.02X+0.12X-0.0135X+Y

X=0.1265X+Y

Y=X-0.1265X

Y=0.8735X

Therefore the operation s that succeed and are free from infections is 0.8735 or 87.35%