Soccer? In a survey of 500 randomly selected Americans, it was determined that 22 play soccer. What is the probability that a randomly selected American plays soccer?

Verified step by step guidance

1. Identify the total number of individuals surveyed, which is 500 in this case.
2. Identify the number of individuals who play soccer, which is 22.
3. Recall that the probability of an event is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes.
4. Set up the probability formula for playing soccer as \(P(\text{plays soccer}) = \frac{\text{number who play soccer}}{\text{total number surveyed}}\).
5. Substitute the values into the formula: \(P(\text{plays soccer}) = \frac{22}{500}\) and simplify if needed.

Key Concepts

Probability

Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this question, it represents the chance that a randomly selected American plays soccer.

Sample and Population

A sample is a subset of individuals selected from a larger group called the population. Here, 500 Americans form the sample, while all Americans represent the population. The sample is used to estimate characteristics, like the probability of playing soccer, for the entire population.

Relative Frequency

Relative frequency is the ratio of the number of times an event occurs to the total number of trials or observations. It serves as an empirical estimate of probability. In this case, the relative frequency of playing soccer is 22 divided by 500, providing an estimate of the probability.