Download A∪ A∩

Please complete as much as you can. 1. Given the set A = { 1, − 5, 0, 15, Δ, 3} and the set B = {2, 4, − 5, Δ} answer the following questions: a. What is A − B (sometimes written as A∖B )? b. What is A∪B ? c. What is A∩B ? d. What do you know about the set C = { } ? e. Define D to be a subset of A. 2. A teacher randomly chooses a two­person team from a group of four students. The first person chosen will be the presenter and the second person will be the researcher. Two of the students, Amir and Aaron, are boys. The other two students, Caitlin and Deniz, are girls. All of the possible outcomes are listed below. a. If we take outcomes 1, 4, 9, and 12 as a subset of the sample space, which of the statements below describes the subset? (Circle all that apply) i.
The subset consists of all the teams not made up of one boy and one girl. ii.
The subset consists of all the teams made up of either all girls or all boys. iii.
The subset consists of all the teams made up of one boy and one girl. iv.
The subset consists of all the teams made up of either all girls or one boy and one girl. 3. Joel has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Joel's Jumble has 2 classical songs, 13 rock songs, and 5 rap songs on it. a. What is P (rock song or rap song) ? (round your answer to two decimal places if necessary) b. What is P (classical song) ? 4. Joe and Maxine are playing a game where they flip a fair coin four times and try to predict the outcomes. Joe thinks that the probability of getting exactly two heads in the four flips is greater than the probability of getting heads on both the first and second flips. Maxine disagrees. She thinks that the two probabilities are equal. The sample space of possible outcomes is listed to the left. H represents heads, and T represents tails. Who is correct? Defend your answer using set notation. 5. Bilal’s favorite colors are red and green. He has 1 red shirt, 1 green shirt, 1 red hat, 1 green scarf, 1 red pair of pants, and 1 green pair of pants. Bilal selects one of these garments at random. Let A be the event that he selects a green garment and let B be the event that he chooses as scarf. a. Which of the following are true? (Circle all that apply) i.
P (A|B) = P (A) ​
The probability that Bilal selects a green garment given that he has chosen a scarf is equal to the probability that Bilal selects a green garment. ii.
P (B|A) = P (B) The probability that Bilal selects a scarf given that he has chosen a green garment is equal to the probability that Bilal selects a scarf. iii.
Events A and B are independent events. iv.
The outcomes of events A and B are dependent on each other. v.
P (A and B) = P (A) • P (B) The probability that Bilal selects a garment that is green and is a scarf is equal to the probability that Bilal selects a green garment multiplied by the probability that he selects a scarf.