A coin is flipped and a number cube is rolled. The tree diagram below shows the possible outcomes. Use the diagram to answer the questions. Coin Number cube heads tails 23 in 10HN 345 2 6 (a) How many outcomes are there? outcome(s) Outcome (heads, 1) (heads, 2) (heads, 3) (heads, 4) (heads, 5) (heads, 6) (tails, 1) (tails, 2) (tails, 3) (tails, 4) (tails, 5) (tails, 6) (b) How many outcomes do not involve rolling 57 outcome(s) (c) How many outcomes involve tails and an odd number? outcome(s) Ten balls numbered from 1 to 10 are placed into a bag. Some are grey and some are white. The balls numbered 1, 3, 5, 7, 8, 9, and 10 are grey. The balls numbered 2, 4, and 6 are white. A ball is selected at random. Let X be the event that the selected ball is white, and let P(X) be the probability of X. Let not X be the event that the selected ball is not white, and let P (not X) be the probability of not X. (a) For each event in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. Event X not X (b) Subtract. Outcomes 1 2 3 4 5 6 7 8 9 10 U 0 1- P(X) = 0 U U 0 0 0 0000000000P(not X) = 0 010 X Probability (c) Select the answer that makes the sentence true. 1-P (X) is the same as (Choose one) P(x) = 0 010 8 9 10 X A fair die is rolled 6 times. What is the probability that a 2 is obtained on at least one of the rolls? Round your answer to three decimal places. 10 X A drawer is filled with 7 black shirts, 5 white shirts, and 10 gray shirts. One shirt is chosen at random from the drawer. Find the probability that it is not a gray shirt. Write your answer as a fraction. X G