Researchers examined all sports-related concussions reported to an emergency room from children ages 5 to 18 in the United States over the course of one year.1 The table below displays the number of concussions in each of the major activity categories. Activity Frequency Bicycles 23,405 Football 20,293 Basketball 11,507 Playground 10,414 Soccer 7667 Baseball 7433 All-Terrain Vehicle 5220 Hockey 4111 Skateboarding 4408 Swimming 3846 Horseback Riding 2648 Total 100,952 (a) Are these results from a population or a sample? (b) What proportion of concussions came from skateboarding? Round your answer to three decimal places. (c) What proportion of concussions came from riding bicycles? Round your answer to three decimal places. (d) Can we conclude that, at least in terms of concussions, riding bicycles is more dangerous to children in the US than skateboarding?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Researchers examined all sports-related concussions reported to an emergency room from children ages 5 to 18 in the United States over the course of one year.1 The table below displays the number of concussions in each of the major activity categories.
| Activity | Frequency |
| Bicycles | 23,405 |
| Football | 20,293 |
| Basketball | 11,507 |
| Playground | 10,414 |
| Soccer | 7667 |
| Baseball | 7433 |
| All-Terrain Vehicle | 5220 |
| Hockey | 4111 |
| Skateboarding | 4408 |
| Swimming | 3846 |
| Horseback Riding | 2648 |
| Total | 100,952 |
(a) Are these results from a population or a sample?
(b) What proportion of concussions came from skateboarding?
Round your answer to three decimal places.
(c) What proportion of concussions came from riding bicycles?
Round your answer to three decimal places.
(d) Can we conclude that, at least in terms of concussions, riding bicycles is more dangerous to children in the US than skateboarding?
1Valasek A and Walter KD, "Pediatric and Adolescent Concussion", Springer, New York (2012).
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