Freshmen GAME 11/10/11 1. A committee of three must be formed from 5 women and 5 men. What is the probability that the committee will be exclusive to one gender? 2. A homework assignment calls for students to write 5 sentences using a total of 10 vocabulary words. If each sentence must use two words and no words can be used more than once, then how many different ways can a student select the words? 3. Aida got 8 SUSHINATORs for her birthday, 4 dictator-style and 4 math-style. Although she got 2 identical dictator-style dolls, the other 2 are unique. And although she got 2 identical mathstyle dolls, the other 2 are unique. In how many distinguishable ways can she line up these 8 dolls on a shelf if she wants to alternate dictator-style and math-style dolls? (Do not complain that you’ve already done this problem because most of you got it wrong ) 4. There are 5 freshmen, 8 sophomores, and 7 juniors in a chess club. A group of 6 students will be chosen to compete in a competition. How many combinations of students are possible if the group is to consist of (a) exactly 3 freshmen? (b) exactly 3 freshmen and 3 sophomores? (c) an equal number of freshmen, sophomores, and juniors? (d) all members of the same class? 5. Janice is threading beads on a string. How many patterns can she create if she has 5 purple beads, 3 green beads, and 2 blue beads, assuming she must use all 10 beads and put them in a circle (left and right do not matter)? Sophomores GAME 11/10/11 1. A point is chosen at random on a segment that is 24 centimeters long. Find the probability that the chosen point is at least five times as far from one endpoint as it is from the other endpoint. Report your answer as a reduced common fraction. 2. A point is chosen at random inside a circle. Find the probability that the chosen point is closer to the circle than it is to the center of the circle. Report your answer as a reduced common fraction. 3. A point is chosen at random from the interior of an isosceles right triangle. Find the probability that the chosen point is closer to the right angle vertex than it is to the other two vertices. Report your answer as a reduced common fraction. 4. In a triangle ABC the measure of angle A is and the measure of angle B is . A ray is chosen at random in the interior of so that the measure of is . If ray meets side at P, find the probability that P is closer to A than it is to B or C. Report your answer as a reduced common fraction. 5. Bart and Homer have identical calculators whose random number generators produce 8-place decimal values between 0 and 1. Each person generates two random numbers and records the sum of his generated values. If you know that Bart’s sum is 1.40000000, what is the probability that Homer’s sum will be larger than Bart’s sum? Report your answer as a decimal rounded to the nearest hundredth. Juniors GAME 11/10/11 1. A city survey found that 47% of teenagers have a part time job. The same survey found that 78% plan to attend college. If a teenager is chosen at random, what is the probability that the teenager has a part time job and plans to attend college? 2. In a school, 14% of students take drama and computer classes, and 67% take drama class. What is the probability that a student takes computer class given that the student takes drama class? 3. In a shipment of 100 televisions, 6 are not defective. If a person buys two televisions from that shipment, what is the probability that both are defective? 4. In the United States, 56% of all children get an allowance and 41% of all children get an allowance and do household chores. What is the probability that a child does household chores given that the child gets an allowance? 5. In a basketball tournament, 3 of the participating teams Lion, Panther and Jaguar have the probabilities of 4/15, 3/10 and 1/5 respectively of winning the tournament. Find the probability that Lion or Jaguar will win the tournament. Seniors GAME 11/10/11 1. A large basket of fruit contains 3 oranges, 2 apples and 5 bananas. If a piece of fruit is chosen at random, what is the probability of getting an orange or a banana? 2. In a class of 30 students, there are 17 girls and 13 boys. Five are A students, and three of these students are girls. If a student is chosen at random, what is the probability of choosing a girl or an A student? 3. In the United States, 43% of people wear a seat belt while driving. If two people are chosen at random, what is the probability that both of them wear a seat belt? 4. In a school, 18% of students take drama and computer classes, and 64% take drama class. What is the probability that a student takes computer class given that the student takes drama class? 5. In a shipment of 100 televisions, 6 are defective. If a person buys two televisions from that shipment, what is the probability that both are defective?