Question

identifying independent events

which scenario depicts two independent events?

• a teacher is calling on students to present their reports. he calls on mario first and then chooses the next presenter from the remaining students.
• the girls basketball team is playing against the boys basketball team. the coach chooses a captain for the girls team and then chooses a captain for the boys team.
• yasmin is picking flowers from a garden to create a bouquet. she picks a flower, keeps it for the bouquet, and then she picks another.
• felipe is making a dentist appointment. first he chooses the day for his appointment, and then he chooses the time from the available openings.

Explanation:

Define independent events

Two events are independent if the occurrence of one event does not affect the probability of the occurrence of the other event. If the outcome of the first event changes the choices or probabilities for the second event, they are dependent.

Analyze the first scenario

"A teacher is calling on students to present their reports. He calls on Mario first and then chooses the next presenter from the remaining students."
Since the second presenter is chosen from the remaining students, the pool of available students has changed. The first choice directly affects who can be chosen next. Therefore, these are dependent events.

Analyze the second scenario

"The girls' basketball team is playing against the boys' basketball team. The coach chooses a captain for the girls' team and then chooses a captain for the boys' team."
The selection of the girls' team captain is made from the girls' roster, and the selection of the boys' team captain is made from the boys' roster. These two groups are completely separate. Choosing a captain for one team has absolutely no effect on the choices or probabilities of choosing a captain for the other team. Therefore, these are independent events.

Analyze the third scenario

"Yasmin is picking flowers from a garden to create a bouquet. She picks a flower, keeps it for the bouquet, and then she picks another."
Because she keeps the first flower (selection without replacement), the total number of flowers and the composition of the garden change before she picks the second flower. Therefore, these are dependent events.

Analyze the fourth scenario

"Felipe is making a dentist appointment. First he chooses the day for his appointment, and then he chooses the time from the available openings."
The available time openings for the second choice depend entirely on which day was chosen first. Since the day chosen restricts or determines the set of available times, these are dependent events.

Answer:

• (A) A teacher is calling on students to present their reports. He calls on Mario first and then chooses the next presenter from the remaining students.
• (B) The girls' basketball team is playing against the boys' basketball team. The coach chooses a captain for the girls' team and then chooses a captain for the boys' team. (Correct answer)
• (C) Yasmin is picking flowers from a garden to create a bouquet. She picks a flower, keeps it for the bouquet, and then she picks another.
• (D) Felipe is making a dentist appointment. First he chooses the day for his appointment, and then he chooses the time from the available openings.