In a certain federal prison, it is known that 2 / 3 of the...

In a certain federal prison, it is known that $2 / 3$ of the inmates are under 25 years of age. It is also known that $3 / 5$ of the inmates are male and that $5 / 8$ of the inmates are female or 25 years of age or older. What is the probability that a prisoner selected at random from this prison is female and at least 25 years old?

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Key Concepts

Probability

Probability is a measure of the likelihood of an event occurring, represented by a number between 0 and 1. It is the foundational concept used to describe outcomes in experiments or situations where uncertainty is involved.

Joint Probability

Joint probability refers to the probability of two (or more) events occurring simultaneously. This concept is essential when determining the likelihood that an item or individual possesses multiple attributes at the same time.

Inclusion-Exclusion Principle

The inclusion-exclusion principle is used to calculate the probability of the union of two events by adding the probabilities of the individual events and then subtracting the probability of their intersection. This method ensures that any overlap between the events is not counted twice.

Complement Rule

The complement rule states that the probability of an event's complement (the event not occurring) is equal to one minus the probability of the event occurring. This is a valuable tool when the probability of the complementary event is easier to compute or provided.

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