Question

Determine whether the statement is true or false. When an event is almost certain to​ happen, its complement will be an unusual event.

Determine the most appropriate conclusion.
A. ​True, the complement would be an unusual event.
B. ​False, the complement of an event has an equal probability as the event.
C. ​False, the probability of the complement has no relation to the probability of the event. D. ​False, the probability of the complement will have a higher probability than the event.

Answer 1

A. True, the complement would be an unusual event.

The compliment of an event is the probability that event doesnt happen, so if the original event has a high probability its compliment will have a low probability.

Answer 2

A. True, the complement would be an unusual event.

Explanation:

The statement is true. When an event is almost certain to happen, its complement is the set of outcomes in which it does not happen. This means that the complement must be very unlikely to happen, or unusual.

Therefore, the most appropriate conclusion is A.

True, the complement would be an unusual event.

The other conclusions are all false:

• B. False, the complement of an event has an equal probability as the event. This is not always true. For example, the probability of rolling a 6 on a die is 1/6, and the probability of not rolling a 6 is 5/6.
• C. False, the probability of the complement has no relation to the probability of the event. This is also not always true. In fact, the probability of the complement is always equal to 1 minus the probability of the event.
• D. False, the probability of the complement will have a higher probability than the event. This is only true if the probability of the event is very low. For example, the probability of winning the lottery is very low, so the probability of not winning the lottery is very high (almost certain).