8. Show that with two fair six sided dice and looking at the total the the following are true: • Having a six on the first dice is independent event with the total being a 7 • Having a six on the first dice is dependent event with the total being an 8 Explain why

19.

115 Students from 3 sections have been asked if they'd rather watch a movie on a Streaming platform or in a movie theater. Results are tallied below.    Section 101 Section 105 Section 107 Total Streaming platform 17 20 23 60 movie theater  21 15 9 45 Total 38 35 32 105 If we choose a student at random, are the events "the student is in Section 101" and "the student prefers streaming platform classes" independent or dependent events? Group of answer choices independent dependent it is impossible to tell from the information given

2. Consider a single roll of a 4-sided die. A. Please give the outcome set for this case B. Please draw the possibility tree for this case C. What is the probability of the die landing on 4?

7. State College is playing a rival team for the football championship. If State's first- string quarterback is healthy, State College has a 75% chance of winning. If they have to start their backup quarterback, their chances of winning drop to 40%. The team physician says that there are a 70% chance that the first-string quarterback will play. a. What is the probability that State will win that game? b. Suppose that you miss the game but you read in the headlines of Sunday's paper that State won. What is the probability that the second-string quarterback started?

4. In a tennis match, with the score at deuce, the game is won by the first player who gets a clear lead of two points. If the probability that given player wins a particular point is 0, and all points are played independently, what is the probability that player eventually wins the game?

Part 1: Say whether the situation involves Independent or Dependent events, and explain why. 1. I roll two fair six-sided dice, and get a 2 and a 5. 2. I'm dealt two cards from a standard deck of cards, and get a 2 and a 5.

1. You select a coin at random from your pocket. You replace the coin and select again. Are your selections independent events? Explain.