Let’s define the following event:
F = Justin stays awake until the end of the Sunday Night Football game
The probability of this event is P(F) = 0.5. Which of the following is a true statement P(F)?
A: Over the course of many, many weeks of watching Sunday Night Football, Justin will stay awake until the end of approximately 50% of the games.
B: During the next two Sunday Night Football games, Justin will stay awake until the end of
exactly one game
Statements A and B are both true.
Statements A and B are both false.
Statement A is true. Since the probability of Justin staying awake until the end of the Sunday Night Football game is 0.5, over the course of many, many games, he is expected to stay awake until the end of approximately 50% of the games.
Statement B is false. The probability of Justin staying awake until the end of each individual Sunday Night Football game is independent of each other. Therefore, the probability of him staying awake until the end of exactly one game out of two games is not necessarily 0.5.
Statement A: Over the course of many, many weeks of watching Sunday Night Football, Justin will stay awake until the end of approximately 50% of the games.
This statement is true based on the given probability of P(F) = 0.5. It means that there is a 50% chance that Justin will stay awake until the end of any given Sunday Night Football game. Over a large number of games watched, it is expected that Justin will stay awake until the end of approximately 50% of the games.
Statement B: During the next two Sunday Night Football games, Justin will stay awake until the end of exactly one game.
This statement cannot be determined based on the given information. The probability of Justin staying awake until the end of the game is 0.5, but it does not specify the outcome for the next two games. Therefore, the truth value of statement B cannot be determined.
Therefore, the answer is: A: Over the course of many, many weeks of watching Sunday Night Football, Justin will stay awake until the end of approximately 50% of the games.
Statement A: Over the course of many, many weeks of watching Sunday Night Football, Justin will stay awake until the end of approximately 50% of the games.
To determine if this statement is true, we can use the given probability: P(F) = 0.5. This means that out of all Sunday Night Football games, Justin will stay awake until the end approximately 50% of the time.
Therefore, statement A is true.
Statement B: During the next two Sunday Night Football games, Justin will stay awake until the end of exactly one game.
To determine if this statement is true, we need more information. The probability given, P(F) = 0.5, refers to the probability of Justin staying awake until the end of a single game, not two games.
Therefore, we cannot determine the truthfulness of statement B based on the given information.
Therefore, the correct answer is:
Statement A is true, and Statement B is unknown.