gordon is a physical therapist who specializes in pediatric leg injuries. his patients differ in age and…

gordon is a physical therapist who specializes in pediatric leg injuries. his patients differ in age and type of injury. knee pain ankle pain 0 - 12 years old 3 3 13 - 19 years old 4 5 what is the probability that a randomly selected patient is 13 - 19 years old or suffers from knee pain? simplify any fractions.

gordon is a physical therapist who specializes in pediatric leg injuries. his patients differ in age and type of injury. knee pain ankle pain 0 - 12 years old 3 3 13 - 19 years old 4 5 what is the probability that a randomly selected patient is 13 - 19 years old or suffers from knee pain? simplify any fractions.

Answer

Explanation:

Step1: Calculate total number of patients

$3 + 3+4 + 5=15$

Step2: Calculate number of 13 - 19 years old patients

$4 + 5 = 9$

Step3: Calculate number of patients with knee pain

$3+4 = 7$

Step4: Calculate number of 13 - 19 years old patients with knee pain

$4$

Step5: Use the addition - rule for probability

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, $A$ is the event of being 13 - 19 years old and $B$ is the event of having knee pain. $P(A)=\frac{9}{15}$, $P(B)=\frac{7}{15}$, $P(A\cap B)=\frac{4}{15}$. Then $P(A\cup B)=\frac{9 + 7-4}{15}=\frac{12}{15}=\frac{4}{5}$

Answer:

$\frac{4}{5}$