Question

the following probability model shows the distribution of injuries of youth baseball players, ages 5 - 14, according to researchers at sportmedbc. complete parts (a) through (d)
(b) what is the probability that a randomly selected baseball injury to a 5 - 14 - year - old is to the face or wrist? interpret this probability
p(face or wrist) = 0.384 (round to three decimal places as needed)
interpret this probability. select the correct choice and fill in the answer box to complete your choice.
a. if 1000 baseball injuries to 5 - 14 - year - olds were randomly selected, one would expect exactly of them to have happened to the face or wrist.
b. if 1000 baseball injuries to 5 - 14 - year - olds were randomly selected, one would expect about 384 of them to have happened to the face or wrist.
(c) what is the probability that a randomly selected baseball injury to a 5 - 14 - year - old is to the head, face, or wrist? interpret this probability
p(head, face, or wrist) = (round to three decimal places as needed.)

Explanation:

Step1: Identify the probabilities

From the table, \(P(\text{Head}) = 0.109\), \(P(\text{Face})=0.332\), \(P(\text{Wrist}) = 0.052\)

Step2: Use the addition rule for mutually - exclusive events

Since the events (injury to head, face, or wrist) are mutually - exclusive (a person can't have an injury in two of these locations simultaneously in the context of a single injury), we use the formula \(P(A\cup B\cup C)=P(A)+P(B)+P(C)\)

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Answer:

\(P(\text{head, face, or wrist}) = 0.493\)