Question 1: Match the letters with the correct statement shown below:

Molly rolls two fair number cubes. Match each event with the correct subset of the sample space. a. {(3, 1), (4, 2), (5, 3), (6, 4)} e. {(2, 5), (5, 2) } b. {(1, 2), (1, 4), (1, 6). f. { (1, 6), (2, 5), (3, 4), (2, 2), (2, 4), (2, 6)} (4, 3), (5, 2), (6, 1)} c. {(2, 6), (3, 4), (3, 6), (4, 3), (4, 4), g. {(2, 6), (3, 5), (3, 6). (4, 4), (4, 5), (4, 5), (4, 6), (5, 4), (5, 6), (6, 2), (4, 6). (5, 3). (5, 4). (5, 5). (5, 6). (6, 3), (6, 4), (6, 5). (6, 6)} (6, 2). (6, 3). (6, 4), (6, 5). (6, 6)} d. {(4, 2), (4, 4), (4, 6), (5, 2), (5, 4), h. {(3, 1), (4, 2). (4, 1). (5, 3), (5, 2), (5, 6). (6, 2), (6, 4), (6, 6)} (5, 1), (6, 4), (6, 3), (6, 2), (6, 1)} 1. The first number is less than 3 and the second number is even. 2. The first number minus the second number equals 2. 3. The sum of the numbers is greater than 7. 4. The product of the numbers is an even number greater than 10.A box contains 60 colored balls: 45 of the balls are purple. and 30 of the purple halls have stars on them. If a purple ball being randomly.r chosen and a hall with stars being randomly chosen are independent events. how many of the 60 colored balls have stars on them? Use conditional probability to justify your answer. Suppose events A and B are independent, HA) 2 0.75. and HR) = 0.5. What is P(A |B). the probability of A given 3? a. 0.25 b. 0.375 c. 0.5 d. 0.75 It is known that 2% of all mice in a laboratory have a genetic mutation. A scientist administers a test to 1000 mice that correctly identies mice that have the mutation 95% of the time (meaning that 95% of the mice that have the mutation have a positive test result). The test also correctly identies mice that do not have the mutation 95% of the time (meaning that 95% of the mice that do not have the mutation have a negative test result). of the mice that test positive, what percent have the mutation? Complete the two-way frequency table for the 1000 mice, and show how to use it to nd the answer. Round to the nearest percent. No Mutation mutation Test negative Total