38. Getting to Work According to a survey, the probability that a randomly selected worker primarily rides a bicycle to work is 0.792. The probability that a randomly selected worker primarily takes public transportation to work is 0.071. (c) What is the probability that a randomly selected worker does not ride a bicycle to work?

Verified step by step guidance

1. Identify the probability that a worker rides a bicycle to work, which is given as \(P(\text{bicycle}) = 0.792\).
2. Recall that the probability that a worker does not ride a bicycle to work is the complement of the probability that they do ride a bicycle.
3. Use the complement rule formula: \(P(\text{not bicycle}) = 1 - P(\text{bicycle})\).
4. Substitute the given value into the formula: \(P(\text{not bicycle}) = 1 - 0.792\).
5. Calculate the result to find the probability that a randomly selected worker does not ride a bicycle to work.

Key Concepts

Probability of an Event

Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1. A probability of 0 means the event cannot happen, while 1 means it is certain. For example, the probability that a worker rides a bicycle to work is 0.792, indicating a high likelihood.

Complement Rule

The complement rule states that the probability of an event not occurring is 1 minus the probability that it does occur. If P(A) is the probability of event A, then P(not A) = 1 - P(A). This rule helps find the probability of the opposite outcome, such as not riding a bicycle to work.

Mutually Exclusive Events

Mutually exclusive events cannot happen at the same time. For example, a worker cannot both ride a bicycle and take public transportation to work simultaneously. Understanding this helps in correctly calculating probabilities without overlap.