Section 7.2 Probability Theory - Show your work (20 points) 8 Three points each. Show the events modeling clearly, and show your work. a. The probability of extreme temperature variations on the following day in a season is 0.1. The probability the viral infection occurs when extreme variation of temperature occurs is 0.6. What is the probability that in a season extreme variation of temperature occurs and the viral infection occurs? b A baseball team finds that it wins with a probability of 0.7 when it bats first. In a season, it plays 10 games. What is the probability that it wins 3 games batting first? Assume that there is equal probability that it would bat first, or it would not bat first. C. The mortality probability of a person after 70 with heart attack is 0.2. The mortality probability of a person dying from car accident is 0.3. Assuming that the two events are independent, what is problem, a person will die from heart attack during car accident? d. What is the probability of selecting a specific name when we randomly select the first capital letter out of 26 capital English letters and permutation of the at least three letters and at most seven letters in a name? e. Find the probability of each outcome when a loaded die is rolled, if a 3 and 4 is twice as likely to appear as each of the remaining 4 numbers on the die