According to a certain country’s department of education, 44.5% of 3-year-olds are enrolled in day care. What is the probability that a randomly selected 3-year-old is enrolled in day care?
The correct answer and explanation is:
The probability that a randomly selected 3-year-old is enrolled in day care can be determined by using the percentage provided. The percentage of 3-year-olds enrolled in day care is 44.5%.
Probability is the likelihood of an event occurring and is expressed as a ratio between the favorable outcomes and the total possible outcomes. In this case, the favorable outcome is a 3-year-old being enrolled in day care, and the total possible outcomes are all 3-year-olds.
The probability is calculated as follows: P(enrolled in day care)=Percentage of 3-year-olds enrolled100=44.5100=0.445P(\text{enrolled in day care}) = \frac{\text{Percentage of 3-year-olds enrolled}}{100} = \frac{44.5}{100} = 0.445
Thus, the probability that a randomly selected 3-year-old is enrolled in day care is 0.445 or 44.5%.
This means that, if you randomly choose a 3-year-old from the population, there is a 44.5% chance they will be enrolled in day care. The remaining 55.5% of 3-year-olds are not enrolled in day care.
This type of calculation assumes that the population of 3-year-olds is representative of the general population, meaning there are no biases in selecting a random 3-year-old. If the 44.5% figure is accurate, this result holds under the conditions given.