A survey finds the probability that a customer prefers Brand X is 0.58. What is the probability that a customer does NOT prefer Brand X, and what is the sum of both probabilities?

If $C$ is an event in a sample space, which of the following is always true about $C$ and its complement $C^{\prime }$?

An inspection report reveals that $20\%$ of portable power banks produced in a certain factory do not meet safety standards. A quality analyst needs at least one defective unit for further testing. If the analyst randomly selects $15$ power banks from a larger batch, what is the probability that at least one of them is defective? Is this probability high enough for the analyst to reasonably expect at least one defective item?

Suppose that the probability that a randomly selected employee's security badge scan fails at the entrance is $0.074$. A company’s system checks badge scans in groups of $5$ employees. The system flags the group only if at least one scan fails. Find the probability that the group of $5$ employees will trigger a flag due to at least one badge failure. Should the company prepare for frequent individual re-checks?

Traffic data show that the probability a commuter drives a car to work is $0.732$. What is the probability that a commuter does not drive a car to work?

A bag contains 4 green, 5 yellow, and 1 red marble. What is the probability of NOT drawing a yellow marble?

A die is rolled. What is the probability that it does NOT show a 2?

A cafe analyzed whether customers tipped based on their payment method. Some customers paid with cash, while others paid by card. The results are shown below:

What is the probability that a randomly selected customer tipped, given that the customer paid with card?

In a survey about preferred types of devices, people were asked whether they prefer touch-screen devices or keypad-based devices. The results are shown below:

Let T represent the event of randomly selecting a person who prefers a touch-screen device.

What does T̄ represent?

Find the value of P(T̄).

According to a recent survey, $73.5\%$ of employees at a tech company are male. Find the probability of randomly selecting an employee who is a female.