A student is taking a​ multiple-choice exam in which each question has two choices. Assuming that she has no knowledge of the correct answers to any of the​ questions, she has decided on a strategy in which she will place two balls​ (marked A and B​) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are six multiple-choice questions on the exam. a) What is the probability that she will get at least five questions​ correct?

A student is taking a multiple-choice exam in which each question has four choices A, B, C, and D. Assume that the student has no knowledge of the correct answers to any of the questions. She has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are 15 multiple-choice questions on the exam. What is the probability that she will get     all 15 questions correct?   at least 10 questions correct?   no questions correct?   no more than 5 questions correct?

In a competition, two people will be selected from four finalists to receive the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the four finalists are Anne, Ben, Collin, and Daisy. The possible outcomes can be represented as follows. АВ, АС, AD, BC, BD, CD, ВА, СА, DA, CВ, DB, DC Here, for example, AD represents the outcome that Anne receives the first prize and Daisy receives the second prize. Let = event that Collin gets first prize Y = event that Daisy gets a prize Z= event that both price winners are boys.

26)

Toward the end of a game of Scrabble you hold the letters D,O,G and Q.  You can choose three of these four letters and arrange them in order in how many different ways?

We survey 200 students, and ask each whether they like donuts, pizza, and/or tacos. Every student liked at least one of them. - 100 students liked donuts - 80 students liked pizza - 100 students liked tacos - 10 students liked all three options How many students liked exactly two of the options? Type your answer.

Four puppies, Bruno, Kitty, O'Reilly, and Sweetie, competed in the Annual Puppies of the World Fair. Prizes were awarded for the top three competitors as follows: first place received a Red Ribbon, second place received a Yellow Ribbon, and third place received a Blue Ribbon. Three members of the audience predicted how the prizes would be awarded. • Lucie predicted that Sweetie would win a Red Ribbon, Kitty would win a Yellow Ribbon, and O'Reilly would win a Blue Ribbon. • Jenn predicted that Bruno would win a Red Ribbon, Sweetie would win a Yellow Ribbon, and O'Reilly would win a Blue Ribbon. • Brenton predicted that Kitty would win a Red Ribbon, Bruno would win a Yellow Ribbon, and Sweetie would win a Blue Ribbon. It turns out that each audience member predicted exactly one prize winner correctly. Determine which dog won which prize.