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.

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.

Step-by-step explanation:

Two events are considered independent of each other when the probability that one event occurs doesn’t in any way affect the probability of the other event occurring.

An example is the probability of flipping a coin and rolling a die.

Choosing a captain for the male and female team won’t in any way affect the outcome of the match.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}