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Conditional probability is a concept used to determine the likelihood of an event occurring given that another event has already happened. It helps in understanding how the probability of an event is impacted by the occurrence of a related event.
In the exercise, we determine the likelihood that a music downloader does not care about copyright. This is a classic example of conditional probability.
The notation for conditional probability is usually given as \( P(A|B) \), which is read as "the probability of event A occurring given that event B has occurred."
In our case, downloading music is event \( D \) and not caring about copyright is event \( C \). The given conditional probability is \( P(C|D) = 0.67 \). This tells us that if someone downloads music, there is a 67% chance that they do not care about the copyright.
This measurement is crucial, as it helps us narrow down the circumstances and better predict behavior within a specific group.

The multiplication rule in probability allows us to find the probability of two events happening together. This is particularly useful when dealing with conditional events.
To apply this rule, the formula used is \( P(A \text{ and } B) = P(A) \times P(B|A) \). This means the probability of both event A and B occurring is the product of the probability of A and the conditional probability of B given A.
In the exercise, the task is to find the probability that an Internet user both downloads music (event \( D \)) and doesn't care about copyright (event \( C \)). Using the multiplication rule, this becomes \( P(D \text{ and } C) = P(D) \times P(C|D) \).
Substituting the given values, we have \( P(D \text{ and } C) = 0.29 \times 0.67 \), resulting in a combined probability of 0.1943. This means there is a 19.43% chance that an Internet user will both download music and not care about its copyright status.

Percentage conversion is the process of turning a decimal probability into a percentage, making it easier to understand and interpret the data.
After calculating the joint probability in the previous step, we received a decimal value of 0.1943. Although decimals are functional for precise calculations, percentages offer a more tangible grasp of results.
To convert a decimal to a percentage, simply multiply by 100. For our example, \( 0.1943 \times 100 = 19.43 \% \).
This shows that 19.43% of Internet users download music without caring if it is copyrighted.
This approach is beneficial as it makes statistical information more accessible and relatable for everyday use and communication.