Question

Dirk is a physical therapist who specializes in leg injuries. His patients differ in age and type of injury. Knee pain Ankle pain 3 3 0-12 years old 13-19 years old 2 3 What is the probability that a randomly selected patient is 13-19 years old or suffers from ankle pain? Simplify any fractions.

Answer 1

The probability of a patient being 13-19 years old is

`P=(5)/(11)`

The probability of a patient who suffers from ankle pain is

`P=(6)/(11)`

Then, we use the following formula

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

Where,

`P(A\cap B)=(5)/(11)\cdot(6)/(11)=(30)/(121)`

Then,

`P(A\cup B)=(5)/(11)+(6)/(11)-(30)/(121)=(91)/(121)\approx0.75`

Hence, the probability is 91/121, or 75%.