Exercise Set 7.5: Probability of Dependent Events Find the probability that the following events will occur. 1. A bag contains 9 red marbles and 7 green marbles. What is the probability that you will pull 2 green marbles in a row? 2. A bag contains 12 blue marbles and 10 yellow marbles. What is the probability that you will pull blue marble then a yellow marble? 3. A teacher is randomly distributing 20 chocolate chip and 12 oatmeal cookies to the class. What is the probability that the teacher will hand out 3 chocolate chip cookies in a row? 4. A radio station is randomly giving out 10 free tickets and 18 free t-shirts to group of listeners. What is the probability that the radio station will give away four free tickets in a row? 5. One bag of M&Ms contains 15 green, 20 blue, 14 yellow, 8 brown, and 11 red. What is the probability that you will pull out 2 red and 3 blue M&Ms? 6. One bag of M&Ms contains 20 blue, 30 green, 18 red, 17 yellow, and 15 brown. What is the probability that you will put out 3 green and 2 yellow M&Ms? 7. In a deck there are 52 cards, 4 of which are kings, 4 are queens, and 4 are jacks. What is the probability that you will pull a king, then a queen, then a jack? 8. In a deck there are 52 cards, 4 of which are aces. What is the probability that you will pull 3 aces? 9. A bag of Scrabble letters has 8 Es, 3 Ds, 5 As, and 2 Ts left. What is the probability that you will pull an A and then a T?
10. A bag of Scrabble letters has 3 As, 1 X, 2 Bs and 5 Es left. What is the probability that you will pull an A and then an E? 11. In a deck there are 52 cards, 4 of which are aces, 4 are kings, 4 are queens, 4 are jacks, and are 4 tens. What is the probability of getting an ace-ten straight, which is a fivecard hand with one of each? 12. Ms. Finn needs two students to help read an English passage in her class of 20 boys and 15 girls. If she randomly chooses one student to read, then another, what is the probability that both readers will be boys? 13. Mr. Newton needs two students to help with a science demonstration for his class of 16 boys and 20 girls. If he randomly chooses one student to come to the front of the room. He then chooses a second student from those still seated. What is the probability that both students chosen are girls? 14. You are on a soccer team and want to be goalkeeper in today’s game but it depends on the coach. If Scott coaches, you have a 60% chance, whereas if Andrew coaches, you have a 40% chance. However, Scott coaches 30% of the time. What is the probability that Scott will coach and you will be goalkeeper today? 15. You are on a softball team and want to be pitcher in today’s game but it depends on the coach. If Emily coaches, you have a 50% chance, whereas if Lilia coaches, you have a 70% chance. However, Emily coaches 60% of the time and Lilia coaches the other 40% of the time. What is the probability that Emily will coach and you will be pitching today?
