Question

the following probability model shows the distribution of injuries of youth baseball players, ages 5 - 14, according to researchers at sportmodbc. complete parts (a) through (d)

(a) verify that this is a probability model. choose the correct answer

a. yes, the probability of all events in the table is greater than or equal to 0 and less than or equal to 1, and the sum of the probabilities of all outcomes is less than 1.

b. yes, the probability of all events in the table is greater than 0 and less than 1, and the sum of the probabilities of all outcomes is at least 1.

c. yes, the probability of all events in the table is greater than 0 and less than 1, and the sum of the probabilities of all outcomes equals 1.

d. yes, the probability of all events in the table is greater than or equal to 0 and less than or equal to 1, and the sum of the probabilities of all outcomes equals 1.

(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) = (round to three decimal places as needed.)

Explanation:

Step1: Calculate the sum of probabilities

We need to check if the sum of all probabilities is equal to 1.

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Also, each probability \(0.109,0.332,0.052,0.159,0.112,0.236\) is between \(0\) and \(1\) (inclusive).

Step2: Calculate \(P(\text{face or wrist})\)

For mutually - exclusive events \(A\) (injury to face) and \(B\) (injury to wrist), the formula \(P(A\cup B)=P(A)+P(B)\) is used.
Here \(P(\text{face}) = 0.332\) and \(P(\text{wrist})=0.052\)

$$P(\text{face or wrist})=0.332 + 0.052=0.384$$

Answer:

For part (a), the answer is D. For part (b), \(P(\text{face or wrist}) = 0.384\)