[NW] Baseball Injuries The following probability model shows the distribution of injuries of youth baseball players, ages 5–14, according to researchers at SportsMedBC.


c. What is the probability that a randomly selected baseball injury to a 5–14-year-old is the head, face, or wrist? Interpret this probability.

Verified step by step guidance

1. Identify the probabilities associated with injuries to the head, face, and wrist from the given probability model. These should be provided as individual probabilities or proportions for each injury type.
2. Add the probabilities of the head, face, and wrist injuries together to find the combined probability. Mathematically, this is expressed as: \(P(\text{head or face or wrist}) = P(\text{head}) + P(\text{face}) + P(\text{wrist})\).
3. Ensure that the injury categories are mutually exclusive so that adding the probabilities directly is valid. If there is any overlap, adjust accordingly to avoid double counting.
4. Calculate the sum of these probabilities to get the total probability that a randomly selected injury is to the head, face, or wrist.
5. Interpret the resulting probability as the likelihood that a randomly chosen injury from the population of 5–14-year-old baseball players affects either the head, face, or wrist. This value will be between 0 and 1, where a higher value indicates a greater chance of these injuries occurring.

Key Concepts

Probability and Probability Models

Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1. A probability model assigns probabilities to all possible outcomes in a sample space, ensuring they sum to 1. Understanding this helps calculate the chance of combined events, like injuries to specific body parts.

Addition Rule for Probability

The addition rule is used to find the probability of the union of two or more events. If events are mutually exclusive, their probabilities can be added directly. This rule is essential when calculating the probability that an injury is to the head, face, or wrist by summing their individual probabilities.

Interpretation of Probability

Interpreting probability involves explaining what the calculated value means in context. For example, a probability of 0.3 means there is a 30% chance that a randomly selected injury affects the head, face, or wrist. This helps relate abstract numbers to real-world scenarios.