5 . State whether or not the following events are dependent or independent. Explain your reason a) A regular six-sided red die and a regular six-sided black die are rolled. The red die lands on 3 and the sum of the two dice is greater than 8. b) A heart is drawn from a standard deck of 52 playing cards. Another card is drawn from the deck without replacing the first card. c) A face card is drawn from a standard deck of 52 playing cards. Another card is drawn from the deck after replacing the first card. Explain whether the two events in the following experiments are mutually exclusive or not mutually exclusive. If it is not mutually exclusive, provide an example. a) Experiment I involves rolling two fair dice. Event X is rolling a sum of 5. Event Y is rolling sum of 9. b) Experiment II involves randomly drawing a card from a standard deck. Event X is drawing a heart. Event Y is drawing a Jack. c) Experiment III involves randomly choosing a marble from a bag of solid coloured marbles. Event X is choosing a red marble. Event Y is choosing a green marble. d) Experiment IV involves randomly selecting one number from 1 to 10 inclusive. Event X is selecting an odd number. Event Y is selecting a number that is composite.Leave your final answers in fraction form unless otherwise sta 1. The probability of an event occurring is - . Determine the odds against the event occurring. Use the following information to answer the next question. A survey of Alberta students was used to estimate the percentage of students who participate in school and non-school athletics, as well as the percentage who do not participate in any athletics. The results of the survey are shown in the Venn diagram below. Participation in School and Non-School Athletics School Non - School 15% 38% 26% 21% 2. The odds in favour of randomly selecting an Alberta student who participates in school athletics are: 3. A game has three possible outcomes: A, B, or C. If P(A) = 0.6 and P(B) - 0.3, what is the probabilit of event C? Use the following information to answer the next question. A newspaper article claimed that a new medication doubled the probability of successful treatment compared to an older medication. The article claimed that the odds of the older medication being successful in treatment were 2:5, and that the new odds of success are 4:5 4. Explain whether or not the article's claims are accurate.7. Denis has 15 coins in his pocket, and 6 of them are toonies. He reaches into his pocket and pulls out a coin at random. Determine the probability of the coin not being a toonie. Use the following information to answer the next question. In a children's game, a spinner with five sections numbered 1 to 5 is spun and then a regular six-sided die is rolled. 8. The probability of obtaining an odd number on both the spinner and the die is 9. Teresa is about to draw a card at random from a standard deck of 52 playing cards. If she draws a red card or a face card, she will win a point. Determine the probability Teresa will win a point. Use the following information to answer the next two questions. Sarah is playing with the Italian deck of cards, which is made up of 40 cards: 4 suits (Denari, Clubs, Swords, Cups) of 10 cards each, where each suit has cards numbered 1 to 7, with a jack, queen and king. 10. If one card is randomly selected, then the probability, to the nearest tenth, that it is a Sword or a Club is 11. Determine the probability that two cards selected, without replacement, are both kings. Use the following information to answer the next question. A committee of 4 people is to be randomly selected from a group of 9 people, including Pedro. 12. The probability that Pedro is selected to be on the four-person committee is