Probability

Ten students on a robotics team fill out an information card describing their gender, grade, whether they are currently taking a science course, whether they are on a sports team, and the number of hours they sleep (on average) per night.

1. If an information card is chosen at random, which of the following represents the sample space for the event? 

$$S=\left\{Student \space ID,gender,grade\space level,science \space class,sports\space team,hours \space of\space sleep\right\}$$
$$S=\left\{ S1,S2,S3,S4,S5,S6,S7,S8,S9,S10 \right\}$$
$$S=\left\{S1,S2,S3,S4,S5,S6,S7,S8,S9,S10,male,female,9,10,11,12,yes,no,6,7,8,9\right\}$$

2. The teacher in the robotics club wants to know a little more about her team and chooses a card at random. What is the probability that:
   1. the selected student is female?
   2. the selected student sleeps fewer than 8 hours a night?
   3. the selected student is on a sports team or is taking a science class?
   4. the selected student is not a junior? 

Annie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the probability that Angie and Carlos are seated across from each other? 

Sam created a game where he flips a coin and then rolls a die. What is the probability that Sam will flip a head and then roll a 4? 

You flip a coin three times in a row. Your friend tells you that the sample space for your experiment is just “head/tails.” You know he is incorrect. 

1. Represent the sample space of this experiment visually to help convince your friend, and explain your reasoning. 
2. Is there another way to represent this sample space? Why did you choose your representation?