Problem

In a school survey, \(P(\text{plays}~a~\text{sport}~\text{and}~\text{has}~a~\text{job})\ne~P(\text{plays}~a~\text{sport})P(\text{has}~a~\text{job})\). Interpret this failed independence equality in context without claiming the events are mutually exclusive or guaranteed.

Answer choices

Choose your path.

Preview only

Because both events can occur for one student, P(plays a sport and has an after-school job) equals the product of the marginal probabilities, so the events are independent.

Because P(plays a sport and has an after-school job) is not equal to P(plays a sport)P(has an after-school job), the events are dependent, so playing a sport changes the probability of having an after-school job.

Because P(plays a sport and has an after-school job) is not equal to P(plays a sport)P(has an after-school job), the two events cannot happen for the same student.

Because P(plays a sport and has an after-school job) is not equal to P(plays a sport)P(has an after-school job), having an after-school job guarantees that the student plays a sport.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

In a school survey, \(P(\text{plays}~a~\text{sport}~\text{and}~\text{has}~a~\text{job})\ne~P(\text{plays}~a~\text{sport})P(\text{has}~a~\text{job})\). Interpret this failed independence equality in context without claiming the events are mutually exclusive or guaranteed.

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.