In 2013 about 66 % of fulltime law enforcement workers were...

In 2013 about $66 \%$ of fulltime law enforcement workers were sworn officers, and of those, $88.4 \%$ were male. Females however make up $60.7 \%$ of civilian employees. Choose one law enforcement worker at random and find the following. a. The probability that she is a female sworn officer b. The probability that he is a male civilian employee c. The probability that he or she is male or a civilian employee

In 2013 about $66 \%$ of fulltime law enforcement workers were sworn officers, and of those, $88.4 \%$ were male. Females however make up $60.7 \%$ of civilian employees. Choose one law enforcement worker at random and find the following.
a. The probability that she is a female sworn officer
b. The probability that he is a male civilian employee
c. The probability that he or she is male or a civilian employee

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Key Concepts

Addition Rule

The addition rule is used to calculate the probability that at least one of multiple events will occur. This rule involves adding the individual probabilities of the events and then subtracting the probability of their intersection, ensuring that outcomes counted in both events are not double-counted.

Multiplication Rule

The multiplication rule is a fundamental principle used to calculate the joint probability of two or more events occurring together. It states that if the events are dependent, the probability of both occurring is the product of the probability of one event and the conditional probability of the second event given the first.

Probability

Probability quantifies how likely an event is to occur, with values ranging from 0 (impossibility) to 1 (certainty). In decision-making scenarios, it is a foundational concept used to determine the chance of outcomes based on given conditions or known proportions in a population.

Conditional Probability

Conditional probability is the likelihood of an event occurring given that another specific event has already occurred. This concept is especially useful when dealing with subgroups or specific conditions within a larger population, such as determining the probability of selecting a female within a subgroup of sworn officers.

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