Show all steps. Leave your final answers in fraction form unless otherwise stated. 1. The probability of an event occurring is =. Determine the odds against the event occurring. Use the following information to answer the next two questions. A survey of high students was used to estimate the percentage of students who participate in school and non-school extra-curricular activities, as well as the percentage who do not participate in any extra- curricular activities. The results of the survey are shown in the Venn diagram below. Participation in School and Non-School Extra-Curricular Activities School Non - School 15% 38% 26% 219% 2. Determine the odds in favour of randomly selecting a high school student who participates in school extra-curricular activities. 3. Are the participation in school extra-curricular activities and the participation in non-school extra- curricular activities mutually exclusive events? Justify your answer. 4. A game has three possible outcomes: X, Y, or Z. If P(X) = 0.6 and P(Y) = 0.3, what is the probability of event Z?Use the following information to answer the next question. An internet job recruitment company, Companyl, claims on their website that their company doubles the probability of successful job offers compared to another job recruitment company, Company2. The website claimed that the odds of the Company2 being successful in job offers were 2:5, and that Companyl odds of success are 4:5 5. Explain whether or not the website's claims are accurate. 6. State whether or not the following events are dependent or independent. Explain your reasoning. a) Drawing two names out of a hat one at a time b) Spinning 2 spinners at the same time 7. Of 15 rats in a cage, 5 have black fur, 6 have white fur, and the remaining 4 have brown fur. If 3 rats are randomly chosen from the cage, determine the probability that all of the selected rats have brown fur.Use the following information to answer the next question. A child has a box containing 8 toy cars and 6 toy trucks. He reaches in and randomly selects 2 toys, one after the other, without replacement. 8. Determine the probability that the two toys selected are both toy cars. 9. Fred is about to draw a card at random from a standard deck of 52 playing cards. If he draws a black card or a face card, he will win a point. Determine the probability Fred will win a point. Use the following information to answer the next two questions. An 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 3 face cards, a Knave, Knight, and King. 10. If one card is randomly selected, determine the probability that it is a Denari or a Cup.11. Determine the probability that two cards selected, without replacement, are both 7's. Use the following information to answer the next question. A committee of 3 people is to be randomly selected from a group of 8 people, including Sarah. 12. Determine the probability that Sarah is selected to be on the three-person committee