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Anestetic [448]

2 years ago

10

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. P = %

1 answer:

Kryger [21]2 years ago

7 0

Answer:

The probability of not having an infection and the surgery being a success is 0.8478.

Step-by-step explanation:

Hello!

There are several possible outcomes facing surgery to repair a torn tendon:

"Infection" ⇒ P(In)= 0.04

"Repair fail" ⇒ P(F)= 0.12

"both infection and failure" ⇒ P(In∩F)= 0.0078

P(NIn∩S)=?

Where NIn represents "no infection" and S represents "successful surgery"

The event "no infection" is complementary to the event "infection" and so is it's probability P(NIn)= 1 - P(In)= 1 - 0.04= 0.96

The event "successful surgery" is complementary to the event "Repair fail" and so is it's probability: P(S)= 1 - P(F)= 1 - 0.12= 0.88

"Repair fail" ; "successful surgery"; Total

"Infection" : P(In∩F) ; P(In∩S) ; P(In)

"no infection" : P(NIn∩F) ; P(NIn∩S) ; P(NIn)

P(F) ; P(S) ; 1

P(F) = P(In∩F) + P(NIn∩F)

P(NIn∩F) = P(F) - P(In∩F) = 0.12 - 0.0078= 0.1122

P(NIn∩S)= P(NIn) - P(NIn∩F) = 0.96-0.1122= 0.8478

The probability of not having an infection and the surgery being a success is 0.8478.

I hope it helps!

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Answer:

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Step-by-step explanation:

From the question, we are given a triangle HNK with an angle of 90°

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From the above values, obtained in the question, we can see that this is a right angled triangle.

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We can use Pythagoras Theorem of solve for this.

c² = a² + b²

where c = HK = n

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Therefore the value of HK = n = 13

We can also use Law of Cosines as given in the question to solve for this.

a² = b² + c² - 2ac × Cos A

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b = HN = 12

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Step-by-step explanation:

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