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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.

Sagot :

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

[tex]P=\frac{5}{11}[/tex]

The probability of a patient who suffers from ankle pain is

[tex]P=\frac{6}{11}[/tex]

Then, we use the following formula

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

Where,

[tex]P(A\cap B)=\frac{5}{11}\cdot\frac{6}{11}=\frac{30}{121}[/tex]

Then,

[tex]P(A\cup B)=\frac{5}{11}+\frac{6}{11}-\frac{30}{121}=\frac{91}{121}\approx0.75[/tex]

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

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