HOMEWORK 7 - PROBABILITY & EXPECTED VALUE 1. Which of the following pairs of events are mutually exclusive? Explain why. a) Cards: aces and spades b) Sitting down and standing up c) Two dice: odd and even d) Sitting down and scratching your nose 2. A card is chosen at random from a pack of 52 playing cards. What is the probability of a King or a Queen? 3. A card is chosen at random from a pack of 52 playing cards. What is the probability of a King or a Heart? A deck of cards would be helpful 4. A number is chosen at random from the set of two-digit numbers from 10 to 99 inclusive. What is the probability the number contains at least one digit 2? Counting or Chart5. Two fair dice are thrown. What is the probability that the score on the first die is 6 or the score on the second die is 5? Chart is helpful here 6. In a group of 25 boys, 20 play ice hockey and 17 play baseball. They all play at least one of the games. What is the probability that a boy chosen at random from the class plays ice hockey but not baseball? Venn Diagram is perfect for this one O 7. In a class of 35 children, 22 like bananas, 18 like cherries and 13 like strawberries. o 7 of them like bananas and cherries. O 8 of them like bananas and strawberries. O 5 of them like cherries and strawberries. o They all like at least one of the fruits. What is the probability that a child chosen at random from the class likes cherries only? Make your own Venn Diagram! O3. You are off to soccer, and love being the Goalkeeper. but that depends who is the {each today: o with Coach Sam your probability of being Goalkeeper is (3.5 o with Coach Alex your probability of being Goalkeeper is (3.3 o Sam is Coach more often about 5 of every 1|) games. What's the probability of you being a Goalkeeper at today's game? Tree Diagram is perfect to model this situation @ 9. Tina's favorite meal is pasta; followed by ice cream for dessert. Tina's Morn cooks pasta once a week. o If morn cooks pasta, then the probability of Tina getting ice cream dessert is 2.33 o If mom doesn't cook pasta, then the probability of Tina getting ice cream dessert is 13'4 What is the probability that Tina gets ioe cream for dessert