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).
(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.

Explanation:

Step1: Check probability range

In a probability model, for each event \(E\), \(0\leq P(E)\leq1\). Looking at the given probabilities: \(0.109\), \(0.332\), \(0.052\), \(0.150\), \(0.112\), \(0.230\). All of these values satisfy \(0\leq P(E)\leq1\).

Step2: Calculate sum of probabilities

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Answer:

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.