1. A box contains 12 red marbles and 8 black marbles. Two marbles are drawn without replacement from the box. a. Draw a tree diagram to represent the sample space. Repeat with an Area Model. Draw Here: n b. What is the probability that one is red and the other is a black marble ? Explain/Show work: One hundred students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey. Preference Male Female TOTAL Prefers dogs 36 20 56 Prefers cats 10 26 36 No preference 2 6 8 TOTAL 48 52 100 One hundred students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey. Preference Male Female TOTAL Prefers dogs 36 20 56 Prefers cats 10 26 36 No preference 2 8 TOTAL 48 52 l 00 lli_'_'l_l_l' _ Find the probability that a randomly selected student prefers dogs or is female. Enter your answer as a fraction or decimal. P (prefers dogs or is female) = 2. For each situation below, tell whether the events are mutually exclusive. Justify your answer Situation Are they mutually Explain exclusive? (yeso) Rolling a sum of 7 and rolling doubles A magazine contains twelve pages. You open to a random page. Event A is opening to page 11. Event B is opening to page 9. A bag contains ten blue jerseys numbered one to 10.. The bag also contains five navy jerseys numbered one to five. You randomly pick a jersey. Event A is picking a blue jersey. Event B is picking a jersey with a number less than four. 3. Ms. Romero wants to get her class ice cream. She surveys the students in two of her classes to find out what flavor of ice cream students would prefer and gets the following results. Chocolate Strawberry Vanilla Boy 16 6 8 Girl 14 14 6a. Explain/SHOW WORK to determine each of the probabilities below. P(Chocolate)= P(Boy and Strawberry)= P(Girl or Vanilla)= P(Vanilla)= P(Boy |Strawberry)= P(Chocolatel Girl): b. Are the events {boy} and {vanilla} independent? P (A given B) = P (A). Prove mathematically. Show your work. Explain/Show work