According to the U.S. Census Bureau, the probability that a...

According to the U.S. Census Bureau, the probability that a randomly selected worker primarily drives a car to work is $0.867 .$ The probability that a randomly selected worker primarily takes public transportation to work is 0.048 . (a) What is the probability that a randomly selected worker primarily drives a car or takes public transportation to Work? (b) What is the probability that a randomly selected worker neither drives a car nor takes public transportation to Work? (c) What is the probability that a randomly selected worker does not drive a car to work? (d) Can the probability that a randomly selected worker walks to work equal $0.15 ?$ Why or why not?

According to the U.S. Census Bureau, the probability that a randomly selected worker primarily drives a car to work is $0.867 .$ The probability that a randomly selected worker primarily takes public transportation to work is 0.048 .
(a) What is the probability that a randomly selected worker primarily drives a car or takes public transportation to Work?
(b) What is the probability that a randomly selected worker neither drives a car nor takes public transportation to Work?
(c) What is the probability that a randomly selected worker does not drive a car to work?
(d) Can the probability that a randomly selected worker walks to work equal $0.15 ?$ Why or why not?

Key Concepts

Probability Axioms

The probability axioms establish that the probabilities of all possible outcomes in a sample space must sum to one and that each individual probability lies between zero and one. This principle underpins the validation of any computed values, such as ensuring that assigning a probability of 0.15 to an event like walking to work does not conflict with the total available probability when other commuting options are considered.

Mutually Exclusive Events

Mutually exclusive events are those events that cannot occur simultaneously. In the context of this problem, driving a car and taking public transportation are considered mutually exclusive modes of commuting, meaning if one occurs, the other cannot. This property simplifies probability calculations by allowing for direct addition of the probabilities.

Complement Rule

The complement rule in probability is used to compute the likelihood of an event not occurring by subtracting the probability of the event from one. This is applied to find probabilities of complementary events, such as the worker not driving a car or neither driving nor taking public transportation, by taking the complement of the probabilities associated with these events.

Addition Rule

The addition rule in probability states that for two mutually exclusive events, the probability of either event occurring is the sum of their individual probabilities. This concept is used when calculating the probability that a worker either drives a car or takes public transportation, assuming that these two events cannot happen at the same time.

Transcript

Please give Ace some feedback