Probability Practice College students are grouped into this contingency (classification) table: Major Physics Math English Class Freshman Junior Senior (a) If one student is selected, what is the probability the student is either an English major or a junior? (b) If 8 students are selected randomly, what is the probability that exactly 3 math majors are selected? (c) If 3 students are selected randomly, what is the probability of selecting a student from each major? (d) If I student is selected from this group, what are the odds against selecting a freshman? (e) If 5 students are selected randomly, what is the probability of selecting at least 1 English major? 2. In a casino game, a dealer has two decks of cards. She deals a player one card from the first deck and one card from the second deck. (a) What is the probability of dealing the player a king from both decks? (b) What is the probability of dealing a king from the first deck or a king from the second deck? (c) What is the probability of dealing the same denomination from both decks? 3. A tennis club is having a mixed doubles tournament. If 8 women and their husbands sign up for the tournament, how many mixed doubles teams are possible? How many can be formed if no woman is paired with her husband? A jar contains 17 balls marked LOSE and 3 balls marked WIN. You and an opponent take turns randomly selecting a single ball from the bowl. The selected ball is not replaced. The person who selects the third WIN ball wins the game. It does not matter who selects the first two WIN balls. If you draw first, find the probability that you win the game on your fourth selection. 5. A committee of 1 1 people, 6 women and 5 men, is forming a subcommittee that is to be made up of 2 women and 3 men. In how many ways can the subcommittee be formed? 6. Five women and three men are in line to get a flu shot. Assume that these eight people arrived in completely random order. How many ways can they line up so that the three men are all at the end of the line? 7 There are 10 questions on an exam. Each student must answer 7 questions. The first and last questions must be answered. How many combinations of questions are possible under these conditions? 8. Five people are selected randomly at a shopping mall. What is the probability that they all have different birthdays (month and day)? A group consists of 5 men and 8 women. Three people are selected from this group without replacement. Find the probability that there is at least one woman in the group. 10. A jar contains 1 brown candy, 2 red candies, 2 green candies, and 5 yellow candies. Four candies are taken randomly from the bag. What is the probability that there are exactly 2 green candies and I yellow candy? 11. A college department offers 15 courses for its majors. A major must complete 10 of these courses including 3 that are required. How many different curricula are possible for a major in this department
