Question

Which of the following events are equivalent to the event of getting the ball in the hoop at least once? more than one answer may be correct.

a) Getting the ball in the hoop exactly once
b) Missing the hoop on every attempt
c) Getting the ball in the hoop multiple times
d) Getting the ball in the hoop at least twice

Answer 1

The events equivalent to getting the ball in the hoop at least once are getting the ball in the hoop exactly once, multiple times, and at least twice. Missing the hoop on every attempt is not equivalent as it involves no successful attempts.

Step-by-step explanation:

The question asks which of the following events are equivalent to the event of getting the ball in the hoop at least once. The phrase 'at least once' includes any event where the ball goes into the hoop one time or more. Therefore, the events that are equivalent to getting the ball in the hoop at least once would be:

• a) Getting the ball in the hoop exactly once - This is included as at least one success is achieved.
• c) Getting the ball in the hoop multiple times - This also satisfies the condition of at least one success.
• d) Getting the ball in the hoop at least twice - This similarly satisfies having at least one success.

Option b), Missing the hoop on every attempt, is not equivalent since no successes are achieved, whereas 'at least once' requires one or more successful attempts.